A speeding light camera is situated on a light post above the ground and positioned so that
it is aimed at the ground at a 30-degree
angle. It captures the picture of the back
license plate of a car at a 60-degree angle.
The car was 10 feet from the light post on
which the camera was sitting and the camera
is 20 feet away from the back of the car as
shown in the diagram.
Three friends are walking by and are wondering about the height of the camera. They discuss three ways of determining this distance:
• Benita:
Benita knows that tangent 30° = √3. She does the following calculation to find the height of the camera.
�������������� 30° =10��; so the height of the camera is 10
√3
• Malcolm:
Malcom knows that sine 60° =√32. He does the following calculation to find the height of the camera.
�������� 60° =��20; so the height of the camera is 10√3
• Ramon:
Ramon decides to use the Pythagorean Theorem to find the height of the camera since the triangle is a right triangle.
102 + ��2 = 202
��2 = 400 − 100
�� = √300
Did each friend solve the problem correctly? Explain why.
1. Did Benita solve the problem correctly? Explain why.
2. Did Malcolm solve the problem correctly? Explain why.
3. Did Ramon solve the problem correctly? Explain why.
4. Benita decided that she wanted to determine the height of the same triangle. Could she use the ratios from a 30-60-90 triangle to figure out its height? Why or why not?