A boat is heading towards a lighthouse, where Mason is watching from a vertical
1 answer:
The distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.
<h3>What is trigonometry?</h3>Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A boat is heading towards a lighthouse, where Mason is watching from a vertical distance of 122 feet above the water. Mason measures an angle of depression to the boat at point A to be 16°.
We can draw the above situation as a form of a right-angle triangle.
From the figure, the distance between AB is x ft
From the right angle triangle DBC:
tan66 = 122/CB
CB = 54.31 ft
From the right angle triangle DAC
tan16 = 122/AC
AC = 425.46 ft
x = AC - CB
x = 425.46 - 54.31
x = 371.15 ft ≈ 371 ft
Thus, the distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.
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r is the half of the diameter:
200ft : 2 = 100ft
The athlete has to run ca. 5280ft for one mile:
5280 : 628,31≈8,4
The athlete has to run 8,4 laps