Respuesta :
Answer:
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

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:
[tex]\angle A = 30[/tex]
[tex]AB = 2000[/tex]
[tex]\angle ABC = 180 - 33[/tex]
[tex]\angle ABC = 147[/tex]
[tex]\angle BCA = 180 - \angle A - \angle ABC[/tex]
[tex]\angle BCA = 180 - 30 - 147[/tex]
[tex]\angle BCA = 3[/tex]
First, we calculate side length BC as follows:
[tex]\frac{BC}{\sin A} = \frac{AB}{\sin C}[/tex]
So, we have:
[tex]BC =\sin A \times \frac{AB}{\sin C}[/tex]
This gives:
[tex]BC =\sin (30) \times \frac{2000}{\sin (3)}[/tex]
[tex]BC =19107.3[/tex]
Side length CD (i.e. the height of the mountain) is calculated as follows:
[tex]\sin (\angle DBC) = \frac{CD}{BC}[/tex]
[tex]\sin (33) = \frac{CD}{19107.3}[/tex]
Make CD the subject
[tex]CD = \sin (33) \times 19107.3[/tex]
[tex]CD = 10406.58[/tex]
Hence, the height of the mountain is 10406.58 feet.
Read more about angles of elevation at:
https://brainly.com/question/9817377
