On a sunny day, a building and its shadow form the sides of a right triangle. If the hypotenuse is 34 m long and the shadow is 24 m, how tall is the building

Answers

Answer 1

Answer:

Step-by-step explanation:

h=√[34²-24²]=√[(34-24)(34+24)]=√[10×58]=√(5×29)=√145 ≈12 m

Answer 2

The height of the building is 10 meters.

What is the Pythagorean theorem?

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Let's call the height of the building "h".

We can use the Pythagorean theorem to relate the height, shadow, and hypotenuse of the right triangle:

h² + 24² = 34²

Simplifying and solving for h.

h² = 34² - 24²

h² = 676 - 576

h² = 100

h = 10

Therefore,

The height of the building is 10 meters.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

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Related Questions

A machine with velocity ratio of 5 is used to raise a load with an effort of 500N . If the machine is 80% efficient , determine the magnitude of the load.​

Answers

Answer:

Solutions given:

Velocity ratio V.R =5

effort =500N

efficiency =80%

magnitude of load=?

mechanical advantage [M.A ]

we have

efficiency =M.A/V.R*100%

80=M.A./5*100

80/100*5=M.A

M.A.=4

again

we have

M.A =load/effort

4=load/500

load=500*4

load=2000N

the magnitude of the load is 2000N.

Lmk if you understand thanks

Answers

Answer:

y = 100,000 (1 + 0.04) ²⁰

Step-by-step explanation:

Here:

100,000 = original amount.

0.04 = rate (a percent)

and

20 = number of times you need to run the simulation.

The second sail has one side of length 22 feet and another of length 2 feet. Determine the range of possible lengths of the third side of the sail.

Answers

Answer:

20 < L < 24

Step-by-step explanation:

We know that in any given triangle, the length of two sides is always greater than the length of the third side.

Since the sail is a triangle having length of one side as 22 feet and the length of another side as 2 feet, and let L be the length of the third side.

It follows from our triangle rule of sides above that

22 + 2 > L  (1)

22 + L > 2   (2)and

L + 2 > 22   (3)

It follows that from (1)

22 + 2 > L  

⇒  24 > L (4)

It follows that from (2)

22 + L > 2

⇒ L > 2 - 22

⇒ L > - 44  (5) and

It follows that from (3)

L + 2 > 22

⇒ L > 22 - 2

⇒ L > 20  (6)

Since from (5) and (6),

L > -44 and L > 20

and 20 > -44 ⇒ L > 20

⇒ 20 < L (7)

From (4) 24 > L ⇒ L < 24 (8)

Combining (7) and (8), we have

20 < L < 24

So, the possible range of values of the third side are 20 < L < 24

If two triangles have three congruent, corresponding angles, what additional information is needed to prove that the triangles are congruent?

Answers

Answer:

one side length has to be equal in both triangles.

Answer:

To prove that two triangles with three congruent, corresponding angles are congruent, you would need to have at least one set of corresponding sides that are also congruent. You could then use ASA or AAS congruence theorems or rigid transformations to prove congruence.

Step-by-step explanation:

QUICK HELP! ): 20 POINTS!
A group of friends goes Sky diving, using a parachute to fall in a straight line from (1,45) to (3,36). If they keep going in a straight line, at what coordinates will they land on the x-axis?

Answers

Answer:

at x = 11

0 =-4.5X +49.5

x = 49.5/4.5

x = 11

Step-by-step explanation:

x1 y1  x2 y2

1 45  3 36

   

(Y2-Y1) (36)-(45)=   -9  ΔY -9

(X2-X1) (3)-(1)=    2  ΔX 2

   

slope= -4  1/2    

B= 49  1/2    

   

Y =-4.5X +49.5    

Evaluate Sigma 5 n=1 3(-2)^n-1
Answer choices
-93
-33
33
93

Answers

Answer:

93

Step-by-step explanation:

the answer is 93 no -93 i think so

YES OR NO PLS HELP URGENT
If two polygons are similar are they necessarily congruent?
YES OR NO? WITH EXPLANATION

Answers

Answer

Conditions for similar polygons. We say two figures are similar if they have the same shape, but not necessarily the same size. If they also have the same size, we say they are congruent. ... If two figures are similar, then they are also congruent.

What product is positive (2/5)(-8/9)(-1/3)(-2/7). (-2/5)(8/9)(-1/3)(-2/7). (2/5)(8/9)(1/3)(-2/7). (-2/5)(-8/9)(1/3)(2/7)

Answers

Answer:

d

Step-by-step explanation:

a. (2/5)(-8/9)(-1/3)(-2/7)= - 32/945

b. (-2/5)(8/9)(-1/3)(-2/7) = -32/945

c. 2/5 * 8/9 * 1/3 * - 2/7 = - 32/945

d. -2/5 * - 8/9 * 1/3 * 2/7 = 32/945

Answer:

D

Step-by-step explanation:

32/945 is the final answer

What is the slope of the line?

Answers

Answer:

1/2

slope = Δy/Δx

start at (-1,3)  to get to the line from there you can go down 1 ( Δy = -1)

and left 2 (Δx = -2)

-1/-2 = 1/2

Step-by-step explanation:

mary has 17 m of rope. She wishes to cut it in three pieces so that she has 3 m more than amanda, and amanda has 2 m less than Sarah.

Answers

Answer:

Length of Sarah rope    = 6 m

Length of Amanda's rope  = 4 m

Length of Mary's rope  = 7 m

Step-by-step explanation:

Let the length of Sarah rope = x

Length of Amanda's rope= x - 2

Length of Mary's rope = (x - 2 ) + 3 = x - 2 + 3 = x + 1

Length of rope = 17 m

x + x - 2 + x + 1 = 17

Combine like terms

x + x + x - 2 + 1 = 17

       3x  - 1 = 17

Add 1 to both sides

3x = 17 + 1

3x = 18

Divide both sides by 3

x = 18/3

x = 6

Length of Sarah rope = x  = 6 m

Length of Amanda's rope= x - 2 = 6 - 2 = 4 m

Length of Mary's rope =   x + 1 = 6 + 1 = 7 m

Find the sum or difference of the polynomials. Write your answer in descending order (2x2 + 5x – 12) – (-4x2 + 2x+6)

Answers

Answer:

The correct answer is 6x^2 + 3x - 18

Rewrite the expression in the picture in the form k times x^n.

Answers

Answer:

8 x^-2

Step-by-step explanation:

2 sqrt(x) * 4x ^ -5/2

Rewriting

2 x^1/2  * 4x ^ -5/2

2*4 = 8

x^1/2 * x^ -5/2  

We know a^b * a^c = a^(b+c)

x^ 1/2 * x^ -5/2 = x^ (1/2 -5/2 ) = x^ (-4/2) = x^-2

8 x^-2

Does anybody know the answer? I need help

Answers

I saw that this is from 2 weeks ago so it's probaly too late to answer... if you ever have trouble multiplying exponents use symbolab it's an online calculator that's really good (i use it on all my math exams :)

PLEASE HELP! I WILL GIVE YOU BRAINLIEST!

Answers

Answer:

sry, i am doing this for points

Two cars that are 600km apart are moving towards each other. Their speeds differ by 6km per hour and the cars are 123km apart after 4.5 hours. Find the speed of each car

Answers

Answer: [tex]56\ kmph,\quad 50\ kmph[/tex]

Step-by-step explanation:

Given

Two cars are 600 km apart moving towards each other

Difference in their speed is 6 kmph

After 4.5 hr, they are 123 km apart that is, they covered a distance of [tex]600-123=477\ km[/tex] in 4.5 hours

Suppose their speeds is [tex]v_1\ \text{and}\ v_2[/tex]

[tex]\therefore v_1-v_2=6\quad \ldots(i)[/tex]

Also, distance traveled is given by

[tex]\Rightarrow 477=[v_1+v_2]4.5\\\Rightarrow v_1+v_2=106\quad \ldots(ii)[/tex]

Solve, (i) and (ii) , we get [tex]v_1=56\ kmph\ \text{and}\ v_2=50\ kmph[/tex]

Pleasee help me with this!!

Answers

Answer:

#1 is f.

#2 is d.

#3 is a.

#4 is b.

#5 is c.

#6 is g.

#7 is e.

Step-by-step explanation:

The digit "9" is in the ten's place because it is two numbers/spaces left from the decimal. If you make all the other digits "0", you'll be left with a value of 90.

The digit "1" is in the one's place because it is one number/space left from the decimal. Applying the same concept of making all the other digits "0", you'll be left with a value of 1.

The type of digits to the right of the decimal, starting from left to right, are the tenths place, hundredths place, thousandths place, ten-thousandths place, and millionths. Remember and know those digit types based on their position away from the decimal. The value will be there for you to see afterward.

Solve the following system of equations. -5x - 4y= -11 7x + 3y = 18

Answers

Step-by-step explanation:

-5x - 4y= -117x + 3y = 18

-5x +117x = 3y + 4y = 18

112x = 7y = 18

SOMEONE PLEAS HELP ME OUTTTTT!!!

Answers

The answers is 44 I think

Answer:

31 degrees

Step-by-step explanation:

the side with the length of 29 can be seen as the radius of a circle.

and the sin value of an angle is the distance of a point on that circle from the x-axis. as the standard sin function is for the standard circle with radius 1, we need to multiply this by the actual radius.

15 = sin(?)×29

sin(?) = 15/29 = 0.5172...

? = 31.14... degrees ≈ 31 degrees

The president of the math club is conducting a survey to see where the 12th grade class wants to go to their field trip. Instead of asking the whole class, she surveys only the 12th grade members of the math club. She records the choices and plans to present the results to the school principal. what kind of sampling did she use?

Answers

Convenience sampling.

HELP ASAPPP !
select the correct answer from each drop-down menu.​

Answers

Answer:

3.8; 4

Step-by-step explanation:

In this exercise, you're are required to find the missing values by performing some arithmetic calculations.

For the first part;

Let the missing value be X

Translating the word problem into an algebraic expression, we have;

[tex] X = 2000 * 1.9 * 10^{-6} [/tex]

[tex] X = 3.8 * 10^{-3} [/tex]

For the second part;

Let the missing value be Y.

[tex] 3.8 * 10^{-3} = Y * 9.5 * 10^{-4} [/tex]

[tex] X = \frac {3.8 * 10^{-3}}{9.5 * 10^{-4}} [/tex]

[tex] X = 4 [/tex]

Therefore, the complete sentence would be written as follows;

[tex] 3.8 * 10^{-3} [/tex] is 2000 times greater than [tex] 1.9 * 10^{-6} [/tex]. It is also 4 times greater than [tex] 9.5 * 10^{-4} [/tex]

i need help in this plzz

Answers

Answer:

[tex]8x^{4}[/tex]

3n-10

(a÷5)+12

Step-by-step explanation:

Numbers listed as in the picture.

70) 8 * [tex]x^{4}[/tex]= [tex]8x^{4}[/tex]

71) 3 * n -10= 3n-10

72) 12+ a/5= (a÷5)-12

1, Tính:
a,√27 + 7√5 : √2

Answers

Solution:

[tex]\rightarrow\sf \sqrt{27} + 7 \sqrt{5} : \sqrt{2 } \\ = \sf \sqrt{9(3)} + 7 \sqrt{5} : \sqrt{2 } \\ = \sf \sqrt{ {3}^{2} } \times 3 + 7 \sqrt{5} : \sqrt{2} \\ \rightarrow \large\boxed{\sf{\red{3 \sqrt{3} + 7 \sqrt{5} : \sqrt{2} }}}[/tex]

Answer:

[tex]\large\boxed{\sf{\red{3 \sqrt{3} + 7 \sqrt{5} : \sqrt{2} }}}[/tex]

[tex]\color{red}{==========================}[/tex]

✍︎ʜɴǫɴ

✍︎ʀʀʏɴʟʀɴɪɴɢ

ʀ

I need help plz I don’t understand

Answers

Answer:

Step-by-step explanation:

If AD is an altitude, then by definition it drops from the vertex angle (the top angle) and meets the base at a right angle, which measures 90 degrees. That means that 17x + 73 is a right angle:

17x + 73 = 90 and

17x = 17 so

x = 1

Please help ASAP!!
What is the value of x?

Answers

Answer:

45°

Step-by-step explanation:

80 + 55=135

Every type of triangle has 180 degrees.

180-135=45 degrees.

escample: If 600 Students registered for mat 101,300 for Phy 101 while 173 students registered for both mat101 and phy 101 in 2021 first semester, How many Students registered the two course​

Answers

I don't answer the grammar but if you asked how many kids in total (not counting duplicate people that signed up for both) then 1073 student registered for the courses

When the focus and directrix are used to derive the equation of a parabola, two distances were set equal to each other. = StartRoot (x minus x) squared + (y minus (negative p)) squared EndRoot = StartRoot (x minus 0) squared + (y minus p) squared EndRoot The distance between the directrix and is set equal to the distance between the and the same point on the parabola.

Answers

Answer:

The answer is "A point on the parabola  and Focus".

Step-by-step explanation:

[tex]= \sqrt{(x - x)^2 + (y- (-p))^2} = \sqrt{(x-0)^2+ (y-p)^2} \\\\= \sqrt{(0)^2 + (y+p))^2} = \sqrt{(x)^2+ (y-p)^2} \\\\= \sqrt{(y+p))^2} = \sqrt{(x)^2+ (y-p)^2} \\\\= (y+p) = (x)+ (y-p) \\\\= y+p = x+ y-p \\\\=2p=x\\\\=x=2p[/tex]

Whenever the focus and also the guideline are utilized in determining the parabolic formula, two distances have indeed been equal.

The distance from the direction, as well as a parabolic point, was equal to the distance from the center to a parabolic point.

Answer:

The distance between the directrix and a point on the parabola is set equal to the distance between the focus and the same point on the parabola.

Step-by-step explanation:

Hope this helps! :)

Absolute value equations HELP PLEASE! ALGEBRA!

Answers

Answer:

[tex]4.\\\text{E. }x=5, x=-6,\\\\5.\\\text{A. }x=7, x=-3\\\\\text{18.}\\\text{D. No mistakes.}[/tex]

Step-by-step explanation:

For [tex]a=|b|[/tex], there are two cases:

[tex]\begin{cases}a=b,\\a=-b\end{cases}[/tex]

Question 4:

Given [tex]5|2x+1|=55[/tex],

Divide both sides by 5:

[tex]|2x+1|=11[/tex]

Divide into two cases and solve:

[tex]\begin{cases}2x+1=11,2x=10, x=\boxed{5}\\-(2x+1)=11,2x+1=-11, 2x=-12, x=\boxed{-6}\end{cases}[/tex]

Therefore, the solutions to this equation are [tex]\boxed{\text{E. }x=5, x=-6}[/tex].

Question 5:

Given [tex]\frac{1}{2}|4x-8|-7=3[/tex],

Add 7 to both sides:

[tex]\frac{1}{2}|4x-8|=10[/tex]

Multiply both sides by 2:

[tex]|4x-8|=20[/tex]

Divide into two cases and solve:

[tex]\begin{cases}4x-8=20,4x=28, x=\boxed{7}\\-(4x-8)=20, 4x-8=-20, 4x=-12, x=\boxed{-3}\end{cases}[/tex]

Therefore, the solutions to this equation are [tex]\boxed{\text{A. }x=7, x=-3}[/tex]

Question 18:

There are no mistakes in the solution shown. The answer properly isolates the term with absolute value with no algebraic mistakes. Following that, the answer divides the equation into both absolute value cases and solves algebraically correctly. Therefore, the correct answer is [tex]\boxed{\text{D. No mistakes.}}[/tex]

m∠A = (2x + 5)° and m∠B = (3x − 15)°.
Find the measure of each angle (in degrees) of ▱ABCD.

Answers

Answer:

Step-by-step explanation:

We have to assume that ABCD is a parallelogram. If it isn't, leave a note.

Secondly we have to assume that the angles are consecutive. In a parallelogram, consecutive angles are supplementary.

<A + <B = 180

2x + 5 + 3x - 15 = 180

5x - 10 = 180                    Add 10 to both sides

5x = 190                         Divide by 5

x = 190/5

x = 38

A = 2x + 5

A = 2*38 + 5

A = 81

B = 3x - 15

B = 3*38 - 15

B = 99

An _____________________________ is an answer that falls outside of the domain of the function.

Answers

Answer:

irrelevant is the answer for it doesn't belong

Can you guys help me find ST on the left and WY on the right

Answers

Answer:

ST = 17 and WY = 32

Step-by-step explanation:

3

SV is a perpendicular bisector and divides Δ RST into 2 congruent triangles with

ST = SR , that is

7x - 4 = 3x + 8 ( subtract 3x from both sides )

4x - 4 = 8 ( add 4 to both sides )

4x = 12 ( divide both sides by 4 )

x = 3

Then

ST = 7x - 4 = 7(3) - 4 = 21 - 4 = 17

-------------------------------------------------------------------

4

Δ WXY and Δ WXZ are congruent ( both have 3 congruent angles ), then

WZ = WY , that is

9x - 13 = 6x + 2 ( subtract 6x from both sides )

3x - 13 = 2 ( add 13 to both sides )

3x = 15 ( divide both sides by 3 )

x = 5

Then

WY = 6x + 2 = 6(5) + 2 = 30 + 2 = 32

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