Question

UDD Question 6 10 pts Solve for x. Round to the nearest tenth (one decimal place). Just type the number, no unit of measurement. G X 240 DI F 48 Next * Previous​

Answer 1

The answer is;

54.4

Explanation:

The given parameter are;

Triangle ΔFGH = Right triangle

The length of segment
`\overline {FH}` = 48

The measure of ∠HFG = 28°

The measurement required = The measure of segment
`\overline {FG}` = x

The measure of ∠FHG = 90° angle opposite hypotenuse side of a right triangle

Therefore, ∠FGH = 180° - ∠HFG - ∠FHG = 180° - 90° - 28° = 62°

∠FGH = 62°

By sine rule, we have;

`\overline {FH}`/(sin ∠FGH) =
`\overline {FG}`/(sin(∠FHG)

By substituting the known values, we have;

48/(sin 62°) = x/(sin(90°)

sin(90°) = 1, therefore, we have;

x/1 = x = 48/(sin 62°) = 54.4 (by rounding the answer to the nearest tenth)

x = 54.4