Question

A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the road, as shown in the figure. Approximate the length of the pole. Round to the nearest hundredth.

Answer 1

The length of the pole is 19.15 feet.

What is the angle of elevation?

The angle of elevation is the angle created when an observer looks at an object placed above its height in relation to the eye level or the horizontal line. An angle of elevation is, for example, the angle created between the line of sight and the horizontal line when a man on Earth observes the Sun.

Given:

Angle made by straight road = 15°

Angle of elevation of the sun = 57°

Length of the shadow = 75 feet

∠ACB = 90° - 57° = 33°

∠CAB = 57° - 15° = 42°

Using Sine Law to find BC i.e.length of the pole.

$\frac{BC}{sin A} = \frac{AB}{sin C}$

$\frac{BC}{sin 42} = \frac{75}{sin 33}$

$BC= \frac{75sin 42}{sin 33}$

BC ≅ 19.15 feet (to the nearest hundredth.)

Hence, the approximate length of the pole is 19.15 feet.

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