Question

Alice wants to estimate the height of a giraffe that casts a 15-foot shadow. At the same time of day, when the angle of the sun is identical, she casts a 5-foot shadow. How tall is the giraffe if Alice is 5.25 feet tall?

Answer 1

Answer: 15.75ft

Step-by-step explanation

Graphical explanation:

In the drawing, the red color represents the giraffe and the shadow it makes at a certain angle θ from the sun, Alice's shadow is represented by the darker blue color, and the green represents Alice's height. Finally, the clearer blue line is the angle made by the sun.

Based on this, we can see that two triangles are formed. Thus, we can make the following relation based on proportions:

`(h)/(5.25)=(15)/(5)`

where h represents the giraffe's height, 5.25 is Alice's height, 15 is the giraffe's shadow and 5ft is Alice's shadow.

Thus, solving for h:

`h=(15)/(5)\cdot5.25`
`h=3\cdot5.25`
`h=15.75ft`