Question

Hey ok i need help on this question ive been stuck on it for a couple minutes haha

Answer 1

The side s has a length of 4 and side q has a length of 4
`√(3)` ⇒ F

Explanation:

In the 30°-60°-90° triangle, there is a ratio between its sides

side opp (30°) : side opp (60°) : hypotenuse

1 :
`√(3)` : 2

In the given triangle

∵ The side opposite to 30° is s

∵ The side opposite to 60° is q

∵ The hypotenuse is 8

→ Use the ratio above to find the lengths of s and q

side opp (30°) : side opp (60°) : hypotenuse

1 :
`√(3)` : 2

s : q : 8

→ By using cross multiplication

∵ s × 2 = 1 × 8

∴ 2s = 8

→ Divide both sides by 2

∴ s = 4

∴ The length of s is 4

∵ q × 2 =
`√(3)` × 8

∴ 2q = 8
`√(3)`

→ Divide both sides by 2

∴ q = 4
`√(3)`

∴ The length of q is 4
`√(3)`