Question

Find the length of AC . Use that length to find the length ofCD.

What is the length of CD? Round to the nearest tenth.

2.3 cm
4.0 cm
10.7 cm
18.6 cm

Answer 1

To find CD use the trig ratio that relates that side you're looking for to the angle you have and the other side you're given. We have that the reference angle is 30, and we also have the hypotenuse of that right triangle on the left. Solving for AC, which is the side opposite, we will use the sin ratio:
`sin(30)= (AC)/(10)`. 10 sin(30) = AC. Therefore, AC = 5. Now that have that side measure, we can use that along with the reference angle in the right triangle on the right of 25 to find CD, which happens to be the side adjacent to the reference angle. That satisfies our tangent ratio requirements. Our ratio looks like this then:
`tan(25)= (5)/(CD)`. Solving for CD,
`CD= (5)/(tan(25))` and CD = 10.7, the third choice above.