Question

A surveyor wanted to determine the height of a mountain. To do​ this, she determined that the angle of elevation from point A to the top of the mountain is 33​°. She then drove 1400 meters toward the mountain to point B where she determined that the angle of elevation to the top of the mountain was 43​°. How tall is the​ mountain?
The height of the mountain is approximately________m.

Answer 1

Answer: The height of mountain is 2979 m approximately.

Step-by-step explanation:

Since we have given that

Angle of elevation from Point A to the top of mountain = 33°

Angle of elevation from point B to the top of mountain = 43°

Distance between point A and point B = 1400 = d

so, we need to find the height of mountain 'h'.

so, it becomes,

$h=\dfrac{d}{\cot x-\cot y}\\\\h=\dfrac{1400}{\cot 33-\cot 43}\\\\h=\dfrac{1400}{1.54-1.07}\\\\h=\dfrac{1400}{0.47}\\\\h=2978.72$

Hence, the height of mountain is 2979 m approximately.

Answer 2

The height of the mountain is approximately 3023 m.

The information from the question forms a right angle triangle. From the diagram below we can use trigonometric ratios to find the height of the mountain.

Therefore, the 2 triangles form the following ratios;

• tan 43 = h / x
• tan 33 = h / x + 1400

0.93 = h /x

0.65 = h / x + 1400

x = $\frac{h}{0.93}$

0.65 = $\frac{h}{\frac{h}{0.93} +1400 }$

0.65 = $\frac{h}{\frac{h+1302}{0.93} }$

0.65 = $\frac{0.93h}{h+1302}$

cross multiply

0.65h + 846.3  =0.93h

846.3 = 0.93h - 0.65h

h = 846.3/0.28

h  = 3022.5

height of the mountain ≈ 3023 m.

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