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

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.

$\dfrac{f}{\sin F} = \dfrac{d}{\sin D}$

$\dfrac{12~m}{\sin 40^\circ} = \dfrac{d}{\sin 100^\circ}$

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

$d = \dfrac{12~m \sin 100^\circ}{\sin 40^\circ}$

$d = 18.3850... m$

Answer: 18.4 m