How long is her shadow?

Question

Jessica is 65 in. tall and casts a shadow along the ground. A right triangle is formed between the top of Jessica's head, the bottom of Jessica's feet, and the end of Jessica's shadow. The angle formed at the end of her shadow is 40°.

How long is her shadow?

Answer 1

Draw a diagram and use trigonometry. Jessica's height is one leg of the right triangle and is opposite the angle formed at the end of her shadow. We are told that this angle is 40°. What we must find is the length of her shadow, which is the other leg of the right triangle, namely the base. We can use a trig ratio to do this.

 

tan 40° = 65/x

x * tan 40° = 65

x = 65/tan 40°

x = 65/0.84 = 77.38 in

Answer 2

Hi Kc, the tangent of an angle is the opposite side / adjacent side. Here the angle is 40 degrees. Let x represent the length of Jessica's shadow.

 

Then:

 

tan 40 = 65 / x

 

Solve for x:

 

x = 65 / tan 40

 

x = 77.46 inches rounded

 

Questions?