Answer:
d is 8.4 units
m∠E is 40.3°
Step-by-step explanation:
Let us use the cosine rule to find the side d and then use the sine rule to find the measure of angle E
- Cosine rule is d² = e² + f² - 2(e)(f)(cos D)
- Sine rule is [tex]\frac{sinD}{d}=\frac{sinE}{e}=\frac{sinF}{f}[/tex]
In Δ DEF
∵ EF is represented by d
∵ DF = 6 units and is represented by e
∴ e = 6
∵ DE = 9 units and is represented by f
∴ f = 9
∵ m∠D = 65°
- Substitute the values of e, f and m∠D in the cosine rule above
∴ d² = (6)² + (9)² - 2(6)(9)(cos 65°)
∴ d² = 71.35722773
- Take √ for both sides
∴ d = 8.447320743
- Round it to the nearest tenth
∴ d = 8.4 units
Now let us use the sine rule to find m∠E
∵ [tex]\frac{sin(65)}{8.4}=\frac{sin(E)}{6}[/tex]
- By using cross multiplication
∴ 8.4 × sin(E) = 6 × sin(65)
∴ 8.4 sin(E) = 6 sin(65)
- Divide both sides by 8.4
∴ sin(E) = 0.647362705
- Use [tex]sin^{-1}[/tex] to find m∠E
∴ E = [tex]sin^{-1}[/tex] (0.647362705)
∴ m∠E = 40.34305
- Round it to the nearest tenth
∴ m∠E = 40.3°
