A surveyor wants to find the height of a hill. He determines that the angle of elevation to the top of the hill is 50°. He then walks 40
feet farther from the base from the hill and determines that the angle of elevation to the top of the hill is now 30°. Find the height of
the hill (round to the nearest foot).
es
Answers
Answer:
The height of the hill is 45 feet .
Step-by-step explanation:
Refer the attached figure
Let AB be the height of hill
We are given that He determines that the angle of elevation to the top of the hill is 50°
So, [tex]\angle ACB= 50^{\circ}[/tex]
Now He then walks 40 feet farther from the base from the hill and determines that the angle of elevation to the top of the hill is now 30°
So, CD=40 feet
BD=BC+CD=BC+40
[tex]\ADB= 30^{\circ}[/tex]
In ΔACB
[tex]Tan \theta = \frac{Perpendicular}{Base}\\Tan 50^{\circ} =\frac{AB}{BC}\\1.1917 BC=AB ----1[/tex]
In ΔADB
[tex]Tan \theta = \frac{Perpendicular}{Base}\\Tan 30^{\circ} =\frac{AB}{BD}\\\frac{1}{\sqrt{3}}=\frac{AB}{BC+40}\\\frac{1}{\sqrt{3}}(BC+40)=AB----2[/tex]
So,equate 1 and 2
[tex]1.1917 BC=\frac{1}{\sqrt{3}}(BC+40)\\BC=37.59[/tex]
Substitute the value in equation 1
1.1917 (37.59)=AB
44.796=AB
Hence the height of the hill is 45 feet .
Related Questions
PLZZ HELPP!! On Tony's map, the distance from Saint John, NB to St. John's, NL is 21 cm. The actual distance between these two cities is 1050km. What is the scale of Tony's map?
Answers
Answer:
1/5 000 000
Step-by-step explanation:
1050km is equal to 105 000 000cm
105 000 000 ÷ 21= 5 000 000
So the scale is 1/5 000 000.
Find the total cost, to the nearest cent, for a sweater that costs $22.95 with an additional 5.5% sales tax. Show your work.
Answers
Answer:
22.95×1.055≈$24.21
22.95* 1.055= 24.21
plz help urgent ,plz have step by step explanation find a and b
Answers
Answer:
but i didn't understand the root 5 with b on the question
5. Find the measures of the following. Round to the nearest whole number
Answers
Answer:
a - HT = 17
b - ∠T = 62
c - ∠H = 28
a-17
b-62
c-28
Please someone help me
Answers
Answer:
r = 0.046212737
Step-by-step explanation:
A = 14,400 (what your investment originally is)
P = 7,200 (what you want your investment to be)
n = 365 (interest is compounded daily)
t = 15 (15 years)
Plug all of these numbers into the equation, then solve for r
14,400 = 7,200(1 + r/365)^365 · 15
Divide 7,200 on both sides --> 2 = (1 + r/365)^365 · 15
365 · 15 = 5475 --> 2 = (1 + r/365)^5475
5475√(2) = 1 + r/365 (root 5475 both sides to cancel out the exponent)
(5475√(2)) - 1 = r/365 (subtract one from both sides)
((5475√(2)) - 1) · 365 = r (multiply both sides by 365 to isolate r)
Type the left side into the calculator to get r --> 0.046212737.
Hope this helps!
The answer is r= 0.046212737
Given quad overline{PQ}\perp\overline PQ ⊥ PS start overline, P, Q, end overline, \perp, start overline, P, S, end overline \qquad m \angle QPR = 7x - 9^\circm∠QPR=7x−9 ∘ m, angle, Q, P, R, equals, 7, x, minus, 9, degrees \qquad m \angle RPS = 4x + 22^\circm∠RPS=4x+22 ∘ m, angle, R, P, S, equals, 4, x, plus, 22, degrees Find m\angle QPRm∠QPRm, angle, Q, P, R: Solve for PQR and x. PLZ HELP
Answers
Answer: Khan Academy 2020! The answer is 40!
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Math Question (10 Points):
Answers
Answer:
x-axis
Step-by-step explanation:
Answer:
It is the x-axis
Step-by-step explanation:
In a graph, the horizontal part of it is called the x axis.
Here is an definition: horizontal axis of a system of coordinates, points along which have a value of zero for all other coordinates
Help me ASAP for this picture
Answers
Solution: Multiple 16 by 3/4.
12
A triangle has an area of 369.25 square inches. The height of the triangle is 42.2 inches. What is the length of the base of the triangle? A. 17.5 in. B. 35 in. C. 42.7 in. D. 56 in. Please include all work.
Answers
Answer:
A. 17.5 in.
Step-by-step explanation:
The formula for the area of a triangle is 1/2 * (b * h), where h represents the height and b represents the base. We can solve from reverse using area/height = base*2
369.25/42.2 = 8.75
1/2base = 8.75
base = 8.75 * 2
base = 17.5
Answer:
369.25/42.2 = 8.75
1/2base = 8.75
base = 8.75 * 2
base = 17.5
hope I helped you
How would I answer this using a number line to find what the sum of
-2 + 2 =
Answers
Solution: in the picture
hope it helps^°^
Plzz help I’ll mark brainliest
Answers
Answer:
c
Step-by-step explanation:
the correct answer is c
plz mark me brainliest
i’ll mark you brainliest, please show work!! i’ll also give more points
Answers
Answer:
414
Step-by-step explanation
80+10hrs=230
23bacteria:1hr
414bacteria:18hrs
Find the value of x.
Answers
Answer:
D. 15
Step-by-step explanation:
Both equations need the same end result because this is a square:
3x - 15 = 45 - x =
3x - 3x = 45 - x - 3x
0 = 45 - 4x
4x = 60
4x/4 = 60/4 =
X = 15
Check:
3(15) - 15 = 45 - 15
45 - 15 = 45 - 15
30 = 30
What is h decreased by 20
Answers
Answer:
h minus 20
Step-by-step explanation:
This is because decreased means or signifies “-“
Math Question (10 Points):
Answers
Answer:
A
Step-by-step explanation:
Becuase It expands the (2+4)8=2*8+8*4=6*8=48
Hope this helps! <3
Sally’s house is located at (5, −1) and her school is located at (−9, 7). Her best friend Molly lives at
the midpoint of Sally’s house and school. What coordinate represents Molly’s house?
A. (2, −3) B. (−2, 3) C. (3, −2) D. (−3, 2)
Answers
Answer:
B. (−2, 3)
Step-by-step explanation:
To find the midpoint of a segment, add the x-coordinates of the endpoints and divide by 2. Add the y-coordinates of the segments and divide by 2.
x: (5 + (-9))/2 = -2
y: (-1 + 7)/2 = 3
Midpoint: (-2, 3)
Answer: B. (−2, 3)
Answer:
b
Step-by-step explanation:
-9+5=-4÷2=-2
-1+7=6÷2=3
Find the measure of the remote exterior angle. m∠x=(197−5n)°m∠y=(6n+22)°m∠z=(n+7)°
Answers
Answer:
x=127°
Step-by-step explanation:First you have to solve for n and to do so you have to add the interior angles together and equal them to the remote exterior angle.
n+7+6n+22=197-5n
12n+29=197
12n=168
n-14
once you get n you have to plug it into 197-5n
197-5(14)
197-70
127
The required value of exterior angle m∠x is 127.
From figure x is remote exterior angle m∠x=(197−5n)°. and y and z are interior angles m∠y=(6n+22)° and m∠z=(n+7)° respectively. value of x to be determine.
Angle made at outer side of the corner is called exterior angles.
Here, by properties, sum of the interior angle = remoter exterior angle
So,
m∠x = m∠y + m∠z
197−5n = 6n+22+n+7
168 = 12n
n = 14
put n in m∠x
m∠x=(197−5n)°
m∠x=(197−5*14)°
m∠x=(197−70)°
m∠x=127°
Thus, the required value of exterior angle m∠x is 127.
Learn more about exterior angles here:
https://brainly.com/question/2406986
#SPJ5
Nine and one-half less than four and one-half times a number is greater than 62.5. Which of the following represents the solution set of this problem?
(16, positive infinity)
(Negative 16, positive infinity)
(Negative infinity, 16)
(Negative infinity, Negative 16)
Answers
Answer:
{16, +infinity}
Step-by-step explanation:
Represent the number with n
Required
Find the solution set
From the question, we have that;
4½n - 9½ > 62.5
Convert all numbers to decimal
4.5n - 9.5 > 62.5
Add 9.5 to both sides
4.5n - 9.5 + 9.5 > 62.5 + 9.5
4.5n > 72
Multiply both sides by 2
2(4.5n) > 72 * 2
9n > 144
Multiply both sides by ⅑
⅑ * 9n > 144 * ⅑
n > 16
This implies that n ranges to infinity from positive 16;
Hence, the correct answer is {16, +infinity}
plsssssss help me!!!!!!!!!!!!!!!!!!!!!!! it is recommended that for every 8 square feet of surface, a pond should have 2 fish. a pond that has a surface of 72 square feet should contain how many feet?
Answers
Can someone help me with this math problem
Answers
Answer:
B. (m-1)(m-8)
Step-by-step explanation:
The factors of 8 (constant term) are
{(1,8), (2,4)}, from which we see that 1+8 = 9, the absolute value of the coefficient of the second term.
Therefore we can group the expression as
m^2 - 9m + 8
= m^2-m - (8m -8)
then factor each group
= m(m-1) - 8(m-1)
and factor out (m-1)
= (m-1)(m-8)
TELL ME THE FORMULA FOR VOLUME AND SURFACE AREA OF PRISMS
Answers
Answer:
surfacevolume = 1/2 (bh) l
surfacearea = bh + pl
These cones are similar. Find the surface
area of the smaller cone. Round to the
nearest tenth.
Answers
Answer:
33.3
Step-by-step explanation:
attachment help for question c no explanation only answer thank you
Answers
Answer:
Tablets.
Step-by-step explanation:
You didn't want an explanation so....here you go....no explanation.
Hope that helps and maybe earns a brainliest.
Have a great day!
tablets
Choose the property of real numbers that justifies the equation! Photo of questions are below
Answers
Answer:
Multiplicative Identity Property,Associative Property of Addition,Commutative Property of Multiplication,Zero Property of Multiplication
Step-by-step explanation:
The required properties for the given expression of the real numbers are multiplication property, associative property, commutative property, and property of zero multiplication.
Given that,
A number of expressions for the real number are given we have determined the corresponding properties for the arithmetic operation given.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Here,
1.
n.1 = n
It is a unit multiplication property.
2.
(4 + b) + 7 = 4 + (b + 7)
it is associative property of real numbers.
3.
m.9 = 9.m
it is commutative property.
4.
0.c = 0
It is a property of zero multiplication.
Thus, the required properties for the given expression of the real numbers are multiplication property, associative property, commutative property, and property of zero multiplication.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Please help ASAP!!!!!!!!
Answers
Answer:
Balance = $14,723.06
Step-by-step explanation:
Given:
Principal (P) = $15,000
Interest Rate (R) = 7.5%
Time (T) = ¹/12
Monthly payment = $185.49
Required:
Balance of the loan at the end of 3 months using the formula for simple interest.
SOLUTION:
[tex] I = \frac{P.T.R}{100*12} [/tex]
First Month:
Principal => $15,000
Add interest => [tex](\frac{15,000*7.5*1}{100*12} )[/tex] => $93.75
= $15,093.75
Less payment => $185.49
= $14,908.26
Second Month:
Principal => $14,908.26
Add interest => [tex](\frac{14,908.26*7.5*1}{100*12})[/tex] => $93.18
= $15,001.44
Less payment => $185.49
= $14,815.95
Third Month:
Principal => $14,815.95
Add interest => [tex](\frac{14,815.95*7.5*1}{100*12})[/tex] => $92.60
= $14,908.55
Less payment => $185.49
Balance = $14,723.06A shipping container in the shape of a rectangular prism is 60 feet long, 45 1/2 feet wide, and 14 feet tall. What is the volume of the shipping container? A. 2,400 ft.^3 B. 2,730 ft.^3 C. 38.220 ft.^3 D. 76,440 ft.^3 Please include work!!
Answers
Why you ask? Good question, how you solve volume is l•w•h=v (length•width•height=volume) so it was 60•45.5•14=38,200
Hope this helps!
You multiply the width, height, and length.
Width= 45 1/2
Height= 14
Length= 60
45 1/2•14•60= 38,220
What is the length of AC
Answers
(156 - x)/12 = x
12x = 156 - x
13x = 156
x = 12
AC = 156 - 12
AC = 144
Answer:
|AC| = 144
Step-by-step explanation:
The larger triangle (on the left) and the smaller one (on the right) are similar.
Therefore the following equation of ratios is correct:
x 7
---------- = ---------
156 - x 84
Then 84x = 7(156) - 7x, or
91x = 1092, or x = 12
Then the length of AC is 156 - x, or 144
A circle has a radius of 26.85 inches. What is the circumference of this circle? Use 3.14 for pi. Round your final answer to the nearest tenth. Enter your answer as a decimal in the box. the first choose dropdown has :0.25 and 4 then is the scale factor an enlargement or not THE TRIANGLE ON THE LEFT IS 1.5 AND THERE IS AN ARROW GOING INTO A BIGGER TRIANGLE THAT IS 6
Answers
Answer:
Step-by-step explanation:
Circumference of the circle = 2 x pi x r
= 2 x 3.14 x 26.85
= 168.618 Inches
after rounding to nearest tenth, 168.6 inches
Answer:
168.6 inches
Step-by-step explanation:
The formula for finding the circumference of a circle is:
[tex]\pi r2[/tex] (Basically multiplying [tex]\pi[/tex] by the diameter since the radius is half the diameter)
Let's substitute and solve!
3.14(26.85 × 2) =
3.14 × 53.7 =
168.61800............but if we round to the nearest tenth, it will be 168.6 inches!
Hope that helps and maybe earns a brainliest!
Have a great day! > <
U
PLEASE HELP ME!!!!!!!!!!!!
Answers
Answer:
1. 4, 4, 6, 8
2. 5, 11, 3, 1
3. 11, 27, 111
4. [tex]16\sqrt{14}-31[/tex]
5. [tex]20\sqrt{2}-56[/tex]
Step-by-step explanation:
For the tables remember that after you solve any negative number will turn positive
For 4-5 just plug in what is in the parenthesis into x and solve
2. 5,11,3,1
3. 11, 27, 111
__
4. 16\|14 -31
___
5. 20\|2 - 56
Find the measure of the remote exterior angle. m∠x=(197−5n)°m∠y=(6n+22)°m∠z=(n+7)°
A. 14
B. 91
C. 21
D. 127
Answers
Answer:
D. 127°
Step-by-step explanation:
The exterior angle (x) is the sum of the remote interior angles (y, z).
Setupx = y +z
(197 -5n) = (6n +22) +(n +7) . . . . . substituting the given expressions
SolutionEliminating parentheses and collecting terms, we have ...
197 -5n = 7n +29
168 = 12n . . . . . . . . . add 5n-29
14 = n . . . . . . . . . . divide by 12
Then the measure of remote exterior angle x is ...
m∠x = (197 -5(14))° = (197 -70)°
m∠x = 127°
