1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Georgia [21]
3 years ago
14

while visiting a mountain, John approximated the angle of elevation to the top of a hill to be 25 degrees. Alfter walking 350 fe

et closer he guessed that the angle of elevation had increased by 14 degrees. Approx. how tall is the hill?

Mathematics
1 answer:
strojnjashka [21]3 years ago
3 0
There are several ways of going about this problem, but just know that it all boils down to triangles and the rules/laws of triangles.
So we start by making a large right triangle, because the hill is vertical with the horizontal ground, with 25° as the left angle (where John looks up to top), 90° is the right angle (where ground meets hill base). So we see that the top side of the triangle is the hypotenuse, and equals the line of sight from John to hilltop.
Now we've got additional information that if John walks 350ft towards the hill, his angle of elevation increases by 14. So that = 25+14 = 39. How does that possibly help us?? Well now we can make 2 triangles inside of the one we've already made. So that now we have the triangle base split between the left angle of 25° and where he stopped 350ft to the right of that.
Now the supplement of 39 is 141, and the remaining piece of that too left triangle = 180-25-141 = 14. What does that mean? Well now we have a triangle, where we know all 3 angles and 1 side --> we can find another side by the law of sines:
If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of sines states:
a÷sinA = b÷sinB = c÷sinC
We really need the hypotenuse to then find our hill height, so we'll make hypotenuse = side b in attached image. That being so, then its opposite angle (B) = 141. And the top right angle (C) = 14 with its opposite side (c) = 350ft.
Now we only need b÷sinB = c÷sinC
So b/sin141 = 350/sin14 --> b = 350sin141/sin14 = 350×.63/
b = 220.3/.24 = 910.47 ft
Now that's our hypotenuse, so using our original large right triangle, we can use right triangular trig. to solve. Let's make the right side, our hill height, equal to x.
Sin ¥ = opp. side / hypotenuse -->
Sin ¥ = x / hypotenuse
Sin25 = x / 910.5
x = 910.5×sin25 = 910.5×.423
x = 384.8 ft

You might be interested in
if 36 cookies cost $4.00 what is the unit rate in cookies per dollar. Using the same information what is the unit rate for 1 coo
pogonyaev

Answer:

9 cookies per dollar

Step-by-step explanation:

This is a fraction equal to

36 cookies ÷ 4 dollars

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 4

36 cookies ÷ 4

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

4 dollars ÷ 4

=  

9 cookies

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

1 dollar

=  

9 cookies

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

dollar

= 9 cookies per dollar

3 0
3 years ago
Solve the equation using the quadratic formula.<br><br> x^2+4x=-3
Gnom [1K]
(x+3) (x+1) should be it
8 0
3 years ago
Write the verbal sentence as an equation. let y represent the number
viktelen [127]

Answer:

Marcus is picking songs to play during a slideshow. The songs are each 3\dfrac123  

2

1

​  

3, start fraction, 1, divided by, 2, end fraction minutes long. The slideshow is 31\dfrac1231  

2

1

​  

31, start fraction, 1, divided by, 2, end fraction minutes long.

Step-by-step explanation:

8 0
3 years ago
Please help! By what does n mean it means on like a model
Alex787 [66]
Don’t open the link the other person put in, it a virus
7 0
3 years ago
Simplify (6^2)(3^3)(3x6)^4
stealth61 [152]
The answer for that is 102036672
4 0
3 years ago
Read 2 more answers
Other questions:
  • Six less than twice a number is -22
    5·1 answer
  • What did the track star say while doing 360's on the football field​
    13·1 answer
  • Find the perimeter in feet and in yards
    11·1 answer
  • you are riding the bus to school and you realize it is taking longer because of all the stops you are making
    11·1 answer
  • A plane flew 525 miles in 1.75 hours. Find the average speed of the plane.
    7·1 answer
  • HELP me ASAP i need help
    12·1 answer
  • HELP ASAP WILL MARK BRAINLIEST IF RIGHT!
    9·1 answer
  • 3- (2x - 5) &lt; -4(x + 2)​
    15·1 answer
  • This please I fricking can't understand the question<br>.............​
    13·1 answer
  • 5/8+7/8 in simplest form
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!