Question

Adam, who is 5'6" tall, notices his shadow on the sidewalk. If the angle of elevation from the tip of the shadow to the sun is 60°, what is the distance from the tip of the shadow to the top of his head? (round to 2 decimal places)

Answer 1

Answer:

Distance between tip of shadow to top of his head is 6.36 ft

Step-by-step explanation:

Given: Height of Adam = 5 ft 6 inch

           Angle of elevation from tip of shadow to son = 60°

To find: Distance between tip of shadow to top of his head.

Height of Adam in ft = 5.5 ft

Angle of elevation from tip of shadow to sin =   Angle of elevation from tip of shadow to top of his head  

as, Sun is just behind the head of Adam.

Figure is attached.

In ΔABC,

using trigniometric ratio we get,

$sin\,C=\frac{AB}{AC}$

$sin\,60=\frac{5.5}{AC}$

$\frac{\sqrt{3}}{2}=\frac{5.5}{AC}$

$AC=5.5\times\frac{2}{\sqrt{3}}$

$AC=5.5\times\frac{2}{1.73}$

AC = 6.36 ft

Therefore, Distance between tip of shadow to top of his head is 6.36 ft