The height of the Daredevil cliff is approximately 107.225 feet.
Let's denote the height of the Daredevil cliff as h. According to the problem, the beach slopes gently at an angle of 3 degrees from the horizontal. The line to the base of the cliff is a horizontal line along the beach.
From your position on the beach, the line to the top of the cliff creates an angle of 70 degrees with the line to the base of the cliff. Therefore, the angle between the line to the top of the cliff and the horizontal line along the beach is
70−3=67 degrees.
We can use the tangent function to relate the height of the cliff (h), the horizontal distance along the beach (50 feet), and the tangent of the angle (67∘ ):
tan(67∘ )= h/50
Now, solve for h:
h=50⋅tan(67∘ )
Let's calculate this value:
h≈50⋅tan(67∘ )
h≈50⋅2.1445
h≈107.225
Therefore, the height of the Daredevil cliff is approximately 107.225 feet.
Question
The Daredevil cliffs rise vertically from the beach. The beach slopes gently at an angle of 3 feet from the horizontal. Laying at the water's edge, 50 feet from the base of the cliff, you determine your position, and a straight line to the top of the cliff creates an angle of 70 degrees with the line to the base of the cliff. How high is the daredevil cliff?