Bootsmydog52
contestada

A straight road to the top of a hill is 2500 feet long and makes an angle of 12° with the horizontal. Find the height of the hill. Round to the nearest foot.

Respuesta :

oladayoademosu

The height of the hill is 520 ft

The height of the hill, h the length of the road, L and the ground form a right angled triangle with length of the road as the hypotenuse side and the height of the hill as the opposite side to the angle the road makes with the horizontal, Ф.

Now, from trigonometric ratios,

sinФ = h/L

The height of the hill

Making h subject of the formula, we have

h = LsinФ

Since L = 2500 ft and Ф = 12°, thus

h = LsinФ

h = 2500 ft × sin12°

h = 2500 ft × 0.2079

h = 519.78 ft

h ≅ 520 ft to the nearest foot

So, the height of the hill is 520 ft

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