Question

A 5.9 ft-tall girl stands on level ground. The sun is 30 degrees above the horizon.

How long is her shadow?

l=? ft

Answer 1

Concepts and reason

The concept that is required to solve the given problem is tangent of angle trigonometric identity.

First draw the ray diagram of the girl and then use necessary trigonometric identify to find the required quantity (that is shadow length).

Fundamentals

Tangent of angle is expressed as follows:

$\tan \theta = \frac{{{\rm{apposite}}}}{{{\rm{adjacent}}}}$

The ray diagram of the girl is shown in the below figure.

In the above figure h is the height of the girl, l is the length of the shadow, and $\theta$ angle of made by the line to the sun relative to the horizon.

From the ray diagram the tangent of angle is expressed as follows:

$\tan \theta = \frac{h}{l}$

Substitute 5.9 ft for h and 30^o for $\theta$ in the above equation and solve for shadow length l.

$\begin{array}{c}\\\tan {30^{\rm{o}}} = \frac{{5.9{\rm{ ft}}}}{l}\\\\l = 10.2{\rm{ ft}}\\\end{array}$

Ans:

Thus, the shadow length is $10.2{\rm{ ft}}$ .