Answer: 565 feet
This value is approximate.
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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.
For this case we propose a system of equations:
x: Let the variable representing the quantity of Granny Smith apples
y: Let the variable representing the number of Gala apples
According to the statement we have:
From the first equation we have to:
replacing in the second equation:
So, Carl bought 7 Gala apples
On the other hand:
So, Carl bought 12 Granny Smith apples
Answer:
Carl bought 7 Gala apples and 12 Granny Smith apples