Question

Kyung is building a triangular pool in his backyard. He knows that side f is 12 m and that both angles G and F are 40°, which means that angle D is 100°. What is the length of side d? Round the answer to the nearest tenth.

7.6 m
7.8 m
18.4 m
19.0 m

Answer 1

The answer is C. 18.4

Explanation:

Answer 2

Since you know the length of a side (side f) and the measure of its opposite angle (<F), you have enough information to establish the ratio used in the law of sides. Since you also know the measure of angle D, you can find side d.

`(f)/(\sin F) = (d)/(\sin D)`

`(12~m)/(\sin 40^\circ) = (d)/(\sin 100^\circ)`

`d \sin 40^\circ = 12~m \sin 100^\cric`

`d = (12~m \sin 100^\circ)/(\sin 40^\circ)`

`d = 18.3850... m`

Answer: 18.4 m