12.) From a 200-foot observation tower on the beach, a man sights a whale in difficulty. The angle of depression of the whale is 7º. How far is the whale from the shoreline?
We can use trigonometry to solve the problem. The angle of depression of the whale is 7º, which means that the line of sight from the observation tower to the whale makes an angle of 7º below the horizontal line.
Let x be the distance from the whale to the shoreline. Then, we can use the tangent function:
tan 7º = x / 200
Solving for x, we get:
x = 200 tan 7º
Using a calculator, we get:
x ≈ 24.42 feet
So the whale is about 24.42 feet from the shoreline.
Answers & Comments
Step-by-step explanation:
We can use trigonometry to solve the problem. The angle of depression of the whale is 7º, which means that the line of sight from the observation tower to the whale makes an angle of 7º below the horizontal line.
Let x be the distance from the whale to the shoreline. Then, we can use the tangent function:
tan 7º = x / 200
Solving for x, we get:
x = 200 tan 7º
Using a calculator, we get:
x ≈ 24.42 feet
So the whale is about 24.42 feet from the shoreline.