Answer:
m<F = 44°
length of FH = 15
length of GF = 21
Perimeter of ∆FGH = 50
Step-by-step explanation:
✔️Find m<F using the sum of triangle theorem:
The small box indicates angle 90°. Sum of a triangle is 180°. Therefore,
m<F = 180° - (90° + 46°)
m<F = 180° - 136°
m<F = 44°
✔️Find FH using trigonometric function:
Reference angle = 46°
Length of Opposite side = FH = ?
Length of Adjacent side = GH = 14
Apply TOA because we are concerned with the OPP and ADJ sides:
Tan 46° = Opp/Adj
Tan 46° = FH/14
14*Tan 46° = FH
14.4974243 = FH
FH = 15 (approximated to nearest whole number)
✔️Find GH by applying either a trigonometric function or just simply apply pythagorean theorem:
Pythagorean theorem is given as,
c² = a² + b²
c is the longest side (hypotenuse) = GF = ?
a = GH = 14
b = FH = 15
Thus:
GF² = 14² + 15²
GF² = 421
GF = √421
GF ≈ 21 (nearest while number)
✔️Perimeter of ∆FGH = GH + GF + FH
= 14 + 21 + 15
= 50
