What is the angle of elevation to the nearest tenth of a degree to the top of a 35-ft building from 75 ft away?

Guest May 1, 2020

#1**0 **

First, let's form a right triangle with two legs of 75, with 35 being the height of the building, and 75 being the distance that you are standing from the building. Next, we know that the tangent of our angle is opposite/adjacent, which means it is equivalent to:

35 / 75 = 7 / 15

Finally, to get our desired angle, we take the arctan(7/15), which will give us our desired angle. Plugging it into a calculator, we get an angle of:

62.1818607 degrees, **which rounds out to 62.2 degrees **

LuckyDucky May 1, 2020

#4**0 **

Trig

So, we have a right triangle. 35 feet is the measure of the vertical leg, and 75 ft is the measure of the other leg.

The tangent of the angle of elevation would be \(\frac{35}{75}\) . So, tan(x) = 35/75 = 7/15, and 7/15 = arctan(x) + pi with the reference angle, that simplifies to something like 25.0165 degrees + pi with the R.A. I am not the best at this stuff :(

So, I'm just going to randomly calculate the hypotenuse ¯\_(ツ)_/¯

Using the Pythagorean Theorem, we know that \(35^2 \cdot 75^2 = \text{hypotenuse}^2 = 6850\)

Therefore, the hypotenuse of the triangle is the square root of 6850. I just found this to complete the triangle, it's unnecessary :D

CentsLord May 1, 2020