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Fofino [41]
3 years ago
5

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 a

ngle of elevation of the sun.
A.) 6.2°

B.) 37.4°

C.) 53.0°

Mathematics
2 answers:
ivolga24 [154]3 years ago
8 0

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}

xxTIMURxx [149]3 years ago
6 0

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.

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