Question

The length of the slope of a mountain is 2780 m, and it makes
its base?
angle of 14.1° with the horizontal. What is the height of the mountain, relative to
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Answer 1

Answer:

677 m

Explanation:

Using the definition of the sine of an angle, we can write

sin 14.1 = (height of mountain) / (slope length of mountain)

sin 14.1 = H / (2780 m) ---> H = (2780 m) x sin 14.1

= 677 m

Answer 2

The height of the mountain is 677.21 m

The given parameters;

length of the slope, L = 2780 m

angle of inclination, Ф = 14.1°

let the height of the mountain, = h

A simple sketch of the problem is given below;

                    ↓P

                    ↓

                    ↓ h

                    ↓                                            14.1°

                    ↓------------------------------------------------Q

                     

A straight line  joining PQ  is  the hypotenuse of the right triangle.

The height of the right triangle is calculated as follows;

$sin(14.1) = \frac{h}{PQ} \\\\\h = PQ \times sin(14.1)\\\\h = 2780 \times sin(14.1)\\\\h = 677.21 \ m$

Thus, the height of the mountain is 677.21 m

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