Question

Carl is standing at the top of 35 Ft cliff looking down at a rock for motion in the sea. He estimates the angle of depression is 30' . What is the horizonal distance from Carl to the island?

Answer 1

The horizontal distance between Carl and the rock at sea is approximately 60.62ft.

Data;

• Angle = 30 degree
• Opposite = 35
• Adjacent = x

Trigonometric Ratio

Given the angle of depression from his point to the sea, we can use trigonometric ratio to calculate for the horizontal distance from his location to the bottom of the sea.

SOHCAHTOA

Since we have the value of angle and opposite and we need to calculate the adjacent side of the right-angle triangle, we can use the tangent of the angle to this effect.

$Tan\theta = \frac{opposite}{adjacent} \\tan 30 = \frac{35}{x}\\ x = \frac{35}{tan30}\\ x = 60.62ft$

The horizontal distance between Carl and the rock at sea is approximately 60.62ft.

Learn more on trigonometric ratio here;

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