Question

In ΔFGH, the measure of ∠H=90°, the measure of ∠F=18°, and HF = 9.2 feet. Find the length of FG to the nearest tenth of a foot.

Answer 1

9.7 feet

Explanation:

You can use the Law of Sines to solve this problem. The law states:

`(sinA)/(a) = (sinB)/(b) = (sinC)/(c)`

Since the given triangle is ASA (angle-side-angle) and we can use the triangle angle sum theorem to find the third angle (sum of triangle angles is 180 degrees). We can therefore determine that angle G is 72 degrees because 180-90-18 is 72.

According to the diagram, we can input our values into the Law of Sines in order solve for FG. Now we can solve the ratio for FG.

`(sin72)/(9.2) = (sin90)/(FG)`

sin90 is 1, so FG is equal to:

`FG = (9.2)/(sin72)`

FG is equal to 9.67 feet, which is 9.7 when rounded to the nearest tenth of a foot.