Question

A pole tilts toward the sun at a 12° angle from the vertical, and it casts a 20-foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 36°. What is the length of the pole? Round your answer to the nearest tenth.

A) 4.5 ft

B) 7.1 ft

C) 11.8 ft

D) 17.6 ft

Answer 1

The correct answer is option C) 11.8 ft

Explanation:

From the figure attached with this answer shows the pictorial representation of the given scenario.

AB be the pole. pole tilts toward the sun at a 12° angle from the vertical shows AC.

ΔAEC and ΔDEC are two right angled triangle.

By using trigonometric ratios,

tan78 = x/y

x = y *tan(78) -----(1)

tan(36) = x/(20 - y)

x = (20 - y )*tan(36) ------(2)

from (1) and (2) we get,

y *tan(78) = (20 - y )*tan(36)

y*4.7 = 20*0.72 - y*0.72

5.42y = 14.4

y = 2.67 ft

To find x

x = y *tan(78) = 2.67 * 4.7 = 12.56 ft

To find height of pole AC

cos(78) = y/AC

AC = y*cos(78) = 2.67 * 0.208 = 12.74ft

Therefore the correct answer in the given options is C) 11.8 ft

Answer 2

D. 17.6 feet

Explanation:

We are given that the angle made by the pole towards the sun is 12° as shown in the figure below.

So, the angle towards the sun by the shadow is = 90° + 12° = 102°

Now, as the angle of elevation is 36°

We can see from the figure below that the sum of the angles will be 180°.

Thus, x° + 36° + 102° = 180°

i.e. x° = 180° - 138°

i.e x° = 42°

Now, applying the Law of Sines, we have,

`(PA)/(sin36)=(20)/(sin42)`

i.e.
`(PA)/(0.59)=(20)/(0.67)`

i.e.
`PA=(20 * 0.59)/(0.67)`

i.e.
`PA=(11.8)/(0.67)`

i.e.
`PA=17.6`

Hence, the length of the pole is 17.6 feet.