A tree on a hillside casts a shadow c = 235 ft down the hill. (description)

Question

A tree on a hillside casts a shadow c = 235 ft down the hill. If the angle of inclination of the hillside is b = 21° to the horizontal and the angle of elevation of the sun is a = 51°, find the height of the tree. (Round your answer to the nearest foot.)

a and b are next to each other side by side and c is below (in picture shown on assignment)

I am really struggling with this portion of my homework. If someone could show me how to solve this step by step and give the correct answer at the end it would help me greatly on the rest of this assignment. Thank you!

Answer 1

I'm guessing it looks like this:

The difference between 51 and 21 (30°) is the angle in the lower right. The obtuse angle is 90° plus 21° (alternate interior angles plus the right angle of the tree). The top angle is 180° - 111 - 30 = 39°

The Law of Sines is appropriate

sin(30°)/h = sin(39°)/235

cross-multiplying gives: h•sin(39°) = 235•sin(30°)

h = 235•sin(30°)/sin(39°) = 186.71 ft or rounding gives h = 187 ft

Answer 2

The easiest way is using the Law of Sines (it works for any triangle) - https://www.mathsisfun.com/algebra/trig-sine-law.html

angle opposite of the tree = 51 - 21 = 30

angle opposite of the shadow = 180 - 90 - 51= 39

Applying the law of sines:

sin(30)/h=sin(39)/235

solving for h = 186.7 ft.

Hope this helps!