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:

This problem can be solved using trigonomtry, assuming that the figure formed by Adam's shadow and Adam himself is a Right Triangle (as shown in the figure attached).

According to this,  the distance from the tip of the shadow to the top of Adam's head is the hypotenuse $H$ of the triangle, and we already know Adam's height and the angle of elevation. So, the trigonometric function that best works in this case is sine:

$sen(angle)=\frac{Oppositeleg}{hypotenuse}$  

Where the opposite leg is the side of the triangle that is opposite to the $60\º$ angle.

In this especific case:

$sen(60\º)=\frac{5.6feet}{H}$     (1)

In order to know the value of the hypotenuse we have to find  $H$ from equation (1):

$H=\frac{5.6feet}{sen(60\º)}$

$H=6.4663 feet$

Rounding:

$H=6.46 feet$>>>>>This is the distance from the tip of the shadow to the top of Adam's head

Answer 2

This can be solved by forming a triangle. The distance from the tip of the shadow to his head is the hypotenuse of the triangle formed. Since 60 degrees is opposite the height of adam, then hypotenuse can be solved using

Sin(60) = 5.5/ h

H = 5.5/sin(60)

H = 6.35 ft