Question

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Answer 1

Answer:

The height of the tree is 19.81 m

Step-by-step explanation:

Trigonometric Ratios

The ratios between the sides of a right triangle are called trigonometric ratios.

If any of the acute angles is chosen as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides and the hypotenuse.

The image shows a right triangle with a tree and the ground forming a right angle and an elevation angle of 33°.

This angle of 33° has a side of 30.5 m as its adjacent leg and the height of the tree X as the opposite side.

The trigonometric ratio that relates both legs is the tangent:

$\displaystyle \tan 33^\circ=\frac{X}{30.5}$

Solving for X

$X=30.5\cdot \tan 33^\circ$

Using a calculator:

X = 19.81 m

The height of the tree is 19.81 m