Question

A vertical pole 6 feet long casts a shadow 55 inches long. Find the angle of elevation of the sun. Draw a diagram and find the angle of elevation of the sun.

A.) 6.2°

B.) 37.4°

C.) 53.0°

Answer 1

A vertical pole(AB) 6 feet long casts a shadow(CB) 55 inches long as shown in the attached image. Since the angle of elevation of sun is $\angle C$. We hav to find the value of $\angle C$.

Firstly, we will change the dimensions of pole(in feet) to the dimension of shadow( in inches) . So, that the dimensions of pole and shadow are same.

Since, 1 feet = 12 inches.

6 feet = $6 \times 12 = 72$ inches.

Now, let us consider the triangle ABC in the attached image,

We have to find $\angle C$

$tan\Theta =\frac{Perpendicular}{base}$

$\tan C$= $\frac{AB}{BC}= \frac{72}{55}$

= 1.309

$= 52.6^{\circ} = 53^{\circ}$

Answer 2

Length of the pole is = 6 feet=6*12=72 inches

Length of shadow of the pole = 55 inches

Here we use tangent function which relates height and shadow . Let the angle of elevation be x .

$tan x = \frac{height}{shadow}$

$tan x = \frac{72}{55}$

x= 52.6 degree= approx 53 degree

So the correct option is C.