Question

zack is standing at the top of a lookout tower and spotsa a water fountain below. if the lookout tower is 75 feet tall and the angle of depression is 28 what is the horizontal distance between zack and the water fountain

Answer 1

The horizontal distance between zack and the water fountain is 141 feet.

Explanation:

Given:

Height of the lookout tower, h = 75 feet

Angle of depression = 28°

Horizontal distance, d = ?

We know:

$tan \alpha = \frac{Perpendicular}{base}$

Substituting the value we get,

$tan(28) = \frac{75}{d}\\\\0.532 = \frac{75}{d} \\\\d = \frac{75}{0.532}\\ \\d = 141 feet$

Therefore, the horizontal distance between zack and the water fountain is 141 feet.

Answer 2

The horizontal distance between zack and the water fountain is 141 feet.

Calculation of the horizontal distance:

Since the lookout tower is 75 feet tall and the angle of depression is 28

So, we know that

$tan\ 28 = 75\div distance\\\\0.532 = 75 \div distance\\\\distance = 75 \div 0.532$

= 141  feet

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