Question

What are the values of w and x in the triangle below? Round the answers to the nearest tenth.

w = 13.3; x = 10.3
w = 10.8; x = 6.1
w = 13.3; x = 23.6
w = 10.8; x = 16.9

Answer 1

w = 13.3, x= 10.3

First option is correct.

Explanation:

In triangle ABC, we have

`\tan42^(\circ)=(AB)/(BC)\\\\\tan42^(\circ)=(12)/(w)\\\\w=(12)/(\tan42^(\circ))\\\\w=13.3`

Now, in triangle ABD

`\tan27^(\circ)=(AB)/(BD)\\\\\tan27^(\circ)=(12)/(w+x)\\\\13.3+x=(12)/(\tan27^(\circ))\\\\13.3+x=23.6\\\\x=10.3`

Thus, we have

w = 13.3, x= 10.3

First option is correct.