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

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.

Answer 2

Answer:

B. 12.2

Step-by-step explanation: