Question

In ΔFGH, the measure of ∠H=90°, the measure of ∠G=7°, and FG = 5.1 feet. Find the length of HF to the nearest tenth of a foot.

Answer 1

6 Feet

Explanation:

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Answer 2

Side FH of the ∆FGH is 3ft

Explanation:

Given

<H = 90°

<G = 7°

FG = 5.1 ft

Required

Length of HF

To start with, we need to identify the type of triangle, ∆FGH is.

Given that <H is 90°, this means that the triangle is a right angled triangle (See attachment below)

From the attachment, side HF is opposite to <G and the hypothenus (FG) of the triangle is known

This means that side HF can be calculated using one of trigonometric functions.

The function that relates side HF, the hypothenus and <G is the sine function.

Recall that

Sinθ = Opp / Hyp

By comparison

θ = <G = 7°

Opp = opposite = side FH

Hyp = Hypothenus = side FG = 5.1

By substituting these values

Sin(7°) = FH/5.1

Make FH the subject of formula

FH = 5.1 * Sin(7°)

FH = 5.1 * 0.6570

FH = 3.3510

FH = 3ft (Approximated)

Hence, side FH of the ∆FGH is 3ft