Question

You're standing on the ground 7777 meters away from the bottom of a tall tower. The tower itself is 346346 meters tall. What is the angle elevation as you look up to the very top of the tower? Round your answer to the nearest tenth.

Answer 1

88.7°

Explanation:

First, visualize. Assuming that the tower is at a perfectly 90° angle to the ground, you have a right triangle. We will call this triangle ΔABC where A is where you are, B is the top of the tower, and C is the base of the tower. Now we know the following:

∠A = ?

∠B = ?

∠C = 90

a = 346346

b = 7777

c = ?

Note: Triangles are labeled with three pairs of letters: a, b and c and A, B and C. The lower case letters, a, b and c represent the sides, and the upper case letters are the angles that are directly opposite of those sides. (see attached reference)

c is easy, c is the hypotenuse, so you can use the following equation to find the hypotenuse:

a² + b² = c²

Rearranged:

c = ±
`\sqrt{a^(2) +b^(2) }`

Substitute a and b:

c = ±
`\sqrt{346346^(2) +7777^(2) }`

Comes out to ~346433.3 meters.

Now if we use the Law of Sines:

`(a)/(sinA)` =
`(b)/(sinB)` =
`(c)/(sinC)`

We can use c and a, since we're trying to find what angle A is, so the ratio is set up as:

`(346346)/(sinA)` =
`(346433.3)/(sinC)`

Well we know that C = 90, and so sin(90) in degrees (as opposed to radians) is 1. So then the set of equations is now:

`(346346)/(sinA)` =
`(346433.3)/(1)`

Cross Multiply to get rid of the fractions:

346346 = 346433.3 * sin(A)

Divide:

`(346346)/(346433.3)` = sin(A)

Using a calculator, if you take the arcsin of that fraction, you will get what angle A is supposed to be:

arcsin(
`(346346)/(346433.3)` ) = ∠A = 88.7°