Question

A mountain road makes an angle θ = 15.5° with the horizontal direction (Fig. P1.46). If the road has a total length of 11.0 km, how much does it climb? That is, find h.

Answer 1

The height climbed is 2.9 km

Explanation:

This is essentially a problem of trigonometry: in fact, we can think the length of the mountain road as the hypothenuse of a right triangle, of which the height h is the side of the triangle opposite to $\theta$.

We call:

L = length of the mountain road (hypothenuse)

h = height climbed by the person (opposite side)

$\theta=15.5^{\circ}$ (angle of inclination of the road)

We also know that the length of the mountain road is

L = 11.0 km

Therefore, we can use the relationship between hypothenuse and opposite side to find the height climbed by the person:

$h=L sin \theta = (11.0)(sin 15.5^{\circ})=2.9 km$

Learn more about trigonometry and right triangles:

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