It's mid-afternoon on a lovely, sunny day; it's 60°F, and the sun is 60° above the horizon. Rays from the sun strike the still surface of a shallow pond that is 20 cm deep. The rays of sun cast a shadow of a stick that is completely submerged, and stuck in the sandy bottom of the pond. If 10 cm of the stick is above the sand, what is the length of the shadow?

The correct answer is 5.77 cm

Explanation:

Solution

From the question given, let us recall the following,

A sunny day = 60°F and

The sun above the horizon is = 60°

The surface of a shallow pond is = 20 cm deep

The stick above sand = 10 cm

The next step is to find the length of the shadow

Now,

let CD = stick

BC = Length of shadow

Thus,

CD/BC = Tan 60°

BC = CD/Tan 60°

= 10/√3 = 5.77 cm

Therefore, the length of the shadow is 5.77 cm