Answer:
F. [tex] 4, 4\sqrt{3} [/tex]
Step-by-step explanation:
✔️Finding length of side s using:
[tex] cos(\theta) = \frac{adjacent}{hypotenuse} [/tex]
Where,
[tex] cos(\theta) = cos(60) = \frac{1}{2} [/tex]
Adjacent = s
Hypotenuse = 8
Plug in the values
[tex] \frac{1}{2} = \frac{s}{8} [/tex]
Multiply both sides by 8
[tex] \frac{1}{2} \times 8 = \frac{s}{8} \time 8 [/tex]
[tex] \frac{8}{2} = s [/tex]
[tex] 4 = s [/tex]
s = 4
✔️Finding length of side q using:
[tex] sin(\theta) = \frac{opposite}{hypotenuse} [/tex]
Where,
[tex] sin(\theta) = sin(60) = \frac{\sqrt{3}}{2} [/tex]
Opposite = q
Hypotenuse = 8
Plug in the values
[tex] \frac{\sqrt{3}}{2} = \frac{q}{8} [/tex]
Multiply both sides by 8
[tex] \frac{\sqrt{3}}{2} \times 8 = \frac{q}{8} \times 8 [/tex]
[tex] \frac{\sqrt{3}}{1} \times 4 = q [/tex]
[tex] 4\sqrt{3} = q [/tex]
[tex] q = 4\sqrt{3} [/tex]
