From the top of a lighthouse 240 feet high, the angle of depression to a boat out on the water is 23 degrees. Find the distance
1 answer:
Answer: 565 feet
This value is approximate.
===============================================
Explanation:
Imagine you are at the top of the lighthouse, and look straight horizontally outward. Then imagine looking down 23 degrees to spot the boat. This forms the angle of depression.
The adjacent angle complementary to this is 90-23 = 67 degrees. This is the interior angle of the triangle needed, and this angle is at the top of the triangle.
tan(angle) = opposite/adjacent
tan(67) = x/240
x = 240*tan(67)
x = 565.4045677977 approximately
x = 565 feet
The diagram is below.
You might be interested in
Here we can first find the area of yard and then subtract the area of vegetable garden to get the required area.
The formula to find area is given by:
Now we find area of yard:
length is 25 ft and width is 15 ft.
Area of yard = 375 ft²
Area of vegetable garden:
length = 8ft and width =8ft
So the vegetable garden is a square.
Area = 8*8
Area of vegetable garden =64 ft²
Area of backyard to be laid with grass = Area of yard-Area of vegetable garden
Area required = 375 -64 = 311 ft²
Answer : The area of backyard in which grass is to be laid is 311 square feet.