Question

The diagram shows triangle ABC with D on AC and E on AB. DE is a straight line. AD = 28 m, AE = 41 m, DE = 22 m and BC = 64 m. Calculate the length CD.

Answer 1

Answer:

CD is approximately 77.55 m

Step-by-step explanation:

I would start by finding the measure of <A using law of cosines

a²=b²+c²-2bc cos A

23²=27²+39²-2(27)(39) cos A

-1721 = -2106 cos A

A = cos^{-1} (\frac{-1721}{-2106})cos−1(−2106−1721)

A = 35.2°

Then I would use law of sines

x/sin 68 = 65/sin 35.2,     x is the length of AC

x = 104.55, then subtract 27 to get the length of CD

CD is approximately 77.55 m