Question

A bird is nested on a tree top that is 14 feet above the ground. The bird looks down at a worm at a 30 angle of depression. How far is the worm from the base of the tree?

Answer 1

Applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.

What is the Tangent Ratio?

Tangent ratio is part of the Trigonometry ratios, which is expressed as, tan ∅ = opposite side / adjacent side in a right triangle.

The information given would form a right triangle, where:

• Reference angle = ∅ = 30°
• Opposite side = 14 ft
• Adjacent side = distance of the worm from the base of the tree = x

Applying the tangent ratio, we would have:

tan 30 = 14/x

x = 14/tan 30

x = 24.2 ft.

Therefore, applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.

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