Question

After a windstorm, a leaning pole makes a 75° angle with the road surface. The pole casts a 15-foot shadow when the sun is at a 45° angle of elevation. About how long is the pole?
11.0 ft.
12.2 ft.
16.7 ft.
20.5 ft.

Answer 1

The answer is 20.5 feet, because when you draw out the triangle and label the angles and given sides and then use the law of sines, you end up with it.

Answer 2

Answer:

Find out the length of the pole.

To prove

As given

After a windstorm, a leaning pole makes a 75° angle with the road surface. The pole casts a 15-foot shadow when the sun is at a 45° angle of elevation.

As shown in the diagram given below.

In the ΔABC

Using the angle sum property of a triangle .

∠A + ∠B + ∠C = 180°

y + 75 + 45 = 180

y = 180 - 120

y = 60°

Let us assume that the length of the pole be x.

Now using the sine rule

$\frac{sin \angle B}{x} = \frac{sin \angle A}{BC}$

BC = 15 foot

$\frac{sin45^{\circ}}{x}= \frac{sin60^{\circ}}{15}$

sin45° =  0.71 (Approx)

sin60° = 0.87 (Approx)

Put in the above

$\frac{0.71}{x}= \frac{0.87}{15}$

$x= \frac{0.71\times 15}{0.87}$

$x= \frac{10.65}{0.87}$

x = 12.2 foot

Therefore the length of the pole is 12.2 foot.