Question

Calculate length of CD
Give answer to 3sf

Answer 1

The length of CD is 12.7 cm

Answer 2

12.7

Using the Pythagorean theorem, you can easily calculate the length of BC.

So:

BC = sqrt(12^2 - 6^2) = sqrt(144 - 36) = sqrt(108) = 10.39230485

Now consider triangle BCD. You know all three angles and one side. Using the law of sines you know that ratio of the sine of each angle over the opposite side is constant. So:

BC/sin(55) = CD/sin(90)

BC/sin(55) = CD/sin(90)

sin(90)BC/sin(55) = CD

1*BC/sin(55) = CD

BC/sin(55) = CD

10.39230485/0.819152044 = CD

12.68666167 = CD

12.7 = CD

Explanation: