Question

Standing on the edge of a cliff 30 m tall, Bob notices a kayak on the lake. If the angle of depression to the kayak is 400, what is the distance, to the nearest meter, from the kayak to the base of the mountain?

Answer 1

• 36 m

Step-by-step explanation:

The vertical height of the cliff, 30 m tall, and the horizontal distance from the kayak to the base of the mountain form a right triangle.

The angle of depression is 40º.

By the alternate interior angles theorem, that depression angle is congruent to the elevation angle from the kayak to the spot where Bob is standing on.

The tangent trigonometric ratio relates the height (30 m) with the distance from the kayak to the base of the mountain:

• tan(40º) = height of the cliff / distance from the kayak to the base of the mountain

• tan(40º) = 30 m / x

• x = 30m / tan(40º) ≈ 35.75 m ≈ 36 m