Robert is standing on a cliff and looks down at an angle of depression of 62 degrees to look at a boat. The cliff is 76 feet high. How far is the boat from the cliff? Round your answer to two decimal places. The boat is _________ feet from the cliff.
Let the distance btw d cliff and the boat be L...tan62=76/L..therefore,L=76/tan62..solve it and gt ur anxa
To find the distance between Robert (standing on the cliff) and the boat, we can use trigonometry and the angle of depression.
Let's call the distance between the cliff and the boat "x."
In a right triangle formed by Robert, the boat, and a vertical line from Robert to the cliff, the angle opposite the side "x" is the angle of depression, which is 62 degrees.
Since the cliff is a vertical line and the height of the cliff is 76 feet, the side opposite the right angle is 76 feet.
We can use the tangent function to find "x":
tan(angle) = opposite/adjacent
tan(62 degrees) = 76 feet/x
Now, we can solve for "x":
x = 76 feet / tan(62 degrees)
Using a calculator, we can find the value of the tangent of 62 degrees:
tan(62 degrees) ≈ 1.880726465
76 feet / 1.880726465 ≈ 40.37 feet
Therefore, the boat is approximately 40.37 feet from the cliff.