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
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;
[tex]sin(14.1) = \frac{h}{PQ} \\\\\h = PQ \times sin(14.1)\\\\h = 2780 \times sin(14.1)\\\\h = 677.21 \ m[/tex]
Thus, the height of the mountain is 677.21 m
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