Question

The angle of elevation from the tip of the shadow to the top of the tree is 36°. Find the distance from the top of the tree to the tip of the shadow. Round the answer to the nearest tenth. A. 26. 7 feet b. 30. 2 feet c. 40. 8 feet d. 42. 9 feet.

Answer 1

The expression that represents the required distance is $\mathbf{ s = \frac{h}{0.5878}}$

The given parameters are:

$\mathbf{\theta =36^o}$ --- the angle of elevation to the top of the tree

To do this, we make use of the following representations

• s represents the distance from the tip of the shadow to the top of the tree
• h represents the height of the tree

The distance (s) is then calculated using the following sine ratio

$\mathbf{ sin(\theta) = \frac{h}{s}}$

Make s the subject

$\mathbf{ s = \frac{h}{sin(\theta)}}$

Substitute $\mathbf{\theta =36^o}$

$\mathbf{ s = \frac{h}{sin(36)}}$

Evaluate sin(36)

$\mathbf{ s = \frac{h}{0.5878}}$

The height of the tree is not known.

Hence, the expression that represents the required distance is $\mathbf{ s = \frac{h}{0.5878}}$

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