Question

Yosemite National Park rangers measured the shadow of a redwood tree to be 48 ft. At the same time of the day and in the same area, a geometry teacher 5 ft 6 in tall casts a shadow 3 ft long. Find the height of the tree. (Hint: Draw pictures and convert everything to inches)

Answer 1

Yosemite National Park rangers measured the shadow of a redwood tree to be 48 ft. At the same time of the day and in the same area, a geometry teacher 5 ft 6 in tall casts a shadow 3 ft long. Find the height of the tree.

As the shadows are observed at the same time of the day and in the same area, the angle of elevation is the same.

Let θ be the angle of elevation

Height of the teacher (BC) : 5 ft 6 in = 66 in

Length of teacher's shadow (AC) : 3 ft = 36 in

Height of the tree (DE) : x

Length of tree's shadow (AE) : 48 ft = 576 in

In △ ABC,

tan θ = opposite side / adjacent side = BC / AC = 66 / 36

tan θ = 11 / 6

In △ ADE,

tan θ = DE / AE = x / 576

tan θ = 11 / 6

11 / 6 = x / 576

x = 576 * 11 / 6 = 1056 in

Height of the tree = 88 ft