Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
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.)
- DerealizationLv 52 months agoFavorite Answer
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