Question

When the sun shines at a 30° angle to the ground, Manuel’s shadow is 109 in. long. To the nearest inch, how tall is Manuel?

Answer 1

Answer:

63 inches

Step-by-step explanation:

Given: Manuel’s shadow is 109 inches when the sun shines at a 30° angle to the ground.

To find: Height of Manuel

Solution:

Let AB denotes height of Manuel and BC denotes shadow of Manuel.

$\tan C=\frac{side \,\,opposite \,\,to\,\, the\,\, angle}{side \,\,adjacent \,\,to\,\, the\,\, angle}$

Side opposite to $\angle C$ = AB

Side adjacent to $\angle C$=  BC

$\angle C=30^{\circ}$

$\tan 30^{\circ}=\frac{AB}{BC}\\\frac{1}{\sqrt{3}}=\frac{AB}{109}\\AB=\frac{109}{\sqrt{3}}=62.93\approx 63\,\,inches$