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# Can someone help me with this question?

As shown in the figure below, a cable car carries passengers from a point A, which is 1.2 miles from a point B at the base of a mountain, to a point P at the top of the mountain. The angles of elevation of P from A and B are 𝛼 = 24° and 𝛽 = 65°, respectively. (Round your answers to one decimal place.) ### 1 Answer

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Note that given 𝛽, we can calculate the measures of ∠ABP and ∠APB as follows:

∠ABP = 180 -  𝛽 = 115

∠APB = 𝛽 - 𝛼  = 41

Calculating these angles allows us to use the Law of Sines as follows:

[AP / sin(115) ]= [ 1.2 / sin(41) ]

Solving for AP gives

AP = 1.2[ sin(115) / sin(41) ] ≈ 1.7m

Thus, the distance between A and P is approximately 1.7 miles.

Also note we can drop a perpendicular of height h from point P to the ground, forming a right triangle. This perpendicular is in fact the height of the mountain. Thus, from trig ratios we have

sin(𝛼) = h / 1.7

Solving for h gives

h = 1.7sin(𝛼) ≈ 0.7 miles

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