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Mathematics

Secondary 4 • May 19, 2023

A hurricane produces winds up to a distance of 300 km. A point along the coastline is 450 km from the eye of the hurricane. The sight line makes an angle of 17 degrees with the coastline. What length of coastline experiences these force winds? Include a diagram and give answer to the nearest kilometre.

Thanks in advance for the help

Answer (1)

Alloprof Answer

May 19, 2023

We can see that angle A is a right angle, and we are given that angle B measures 17 degrees. We want to find the length of the coastline (segment BC) that experiences the force winds.
Since we have a right triangle, we can use trigonometry to find the length of BC. In particular, we can use the tangent function:
tan(B) = opposite/adjacent
In this case, BC is the opposite side and AB is the adjacent side.
tan(17°) = BC/450 km
Rearranging the equation, we have:
BC = 450 km * tan(17°)
Calculating the value, we find:
BC ≈ 128.96 km
Therefore, approximately 129 kilometers of coastline will experience the force winds of the hurricane.