Answer:
Side FH of the ∆FGH is 3ft
Step-by-step 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
