Question

To the nearest degree, find an approximate measure of the angle of elevation to the sun when a tree whose height is 32 meters casts a shadow 35 meters long. Enter a number answer only.

Answer 1

Explanation:

the angle of elevation is the angle on the ground at the end of the shadow abs aiming towards the sun.

we know one angle : the 90° between the tree and its shadow (on the ground).

so, we can calculate with Pythagoras the length of the line of sight bergen the end of the shadow and the top of the tree, which is the Hypotenuse of this right-angled triangle.

Hypotenuse² = 32² + 35² = 1024 + 1225 = 2249

Hypotenuse = sqrt(2249) = 47.42362281... m

the height of the tree is the sine of the angle of elevation multiplied by the length of the Hypotenuse (as the radius of the virtual circle).

32 = sin(angle) × sqrt(2249)

sin(angle) = 32/sqrt(2249) = 0.6747692...

angle of elevation = 42.43622979...° ≈ 42°