Question

Jonathan was laying on the ground and enjoying the shade but now the sun is shining

on him. He knows he is 10 yards away from the building that was shading the sun and
that the building is 8 yards high. At what angle does the sunlight hit the ground? Write
only the number rounded to the nearest degree.

Answer 1

38.5°

Explanation:

Given that the height of the building is 8 yard and the distance between Jonathan and the building is 10 yards.

The sun is at the top of the building, let the distance between Jonathan laying on the ground and the top of the building be x. Using Pythagoras:

x² = 10² + 8²

x² = 100 + 64

x² = 164

x = √164 = 12.86 yards

For a triangle with sides a, b, c and their respective opposite angles A, B, and C. The sine rule is given as:

`(a)/(sin(A)) =(b)/(sin(B))=(c)/(sin(C))`

Let the angle that the sunlight hit the ground be y°. The andle between the building and the ground is 90°. Therefore using sine rule:

`(8)/(sin(y))=(12.86)/(sin(90))\\\\sin(y)=(8*sin(90))/(12.86)\\\\sin(y)=0.622\\\\y=sin^(-1)0.622\\\\y = 38.5^0`