A man standing on top of a vertical cliff looking at a canoe out at sea. The angle of depression of the canoe is 25° . If the cliff is 100 meter high, how far from the base of the cliff is the canoe?
To solve this problem, we can use trigonometry. Let's assume that the distance from the base of the cliff to the canoe is x.
Since the angle of depression from the man to the canoe is 25°, we can use tangent (tan) to find the distance. Tangent is defined as opposite/adjacent, in this case, x/100.
So, according to trigonometry:
tan(25°) = x/100
To find x, we can rearrange the equation:
x = 100 * tan(25°)
Using a calculator, we find that x is approximately 45.74 meters.
Therefore, the canoe is around 45.74 meters away from the base of the cliff.