Asurvey team is trying to estimate the height of a mountain above a level plain. from one point on the plain, they observe that the angle of elevation to the top of the mountain is 30 ∘ . from a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 33 ∘ . how high (in feet) is the mountain?

The angle of elevation is simply the angle from the level plain, and the line of sight.

The height of the mountain is 10406.58 feet.

I've attached a diagram that illustrates the scenario.

From the diagram, we have:

First, we calculate side length BC as follows:

So, we have:

This gives:

Side length CD (i.e. the height of the mountain) is calculated as follows:

Make CD the subject

Hence, the height of the mountain is 10406.58 feet.

Read more about angles of elevation at:

link

10406.5937 ft

Step-by-step explanation:

In the figure attached the graph of the problem is shown.

Data for triangle ABC:

∠A = 30°

∠B = 180° - 33° = 147°,

segment AB = 2000 feet long.

∠C = 180° - 30° - 147° = 3°

From law of sines:

AB/sin(C) =  AC/sin(B)

2000/sin(3) =  AC/sin(147)

AC = [2000/sin(3)]*sin(147)

AC = 20813.1875 ft

Using now triangle ADC:

sin(A) = CD/AC

CD = sin(A)*AC

CD = sin(30)*20813.1875

CD = 10406.5937 ft

isi

step-by-step explanation:

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