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Irina-Kira [14]
2 years ago
12

Write your answer in simplest radical form​

Mathematics
1 answer:
Ad libitum [116K]2 years ago
6 0

Answer:

n = 8√2

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 60°

Opposite = 4√6

Hypothenus = n =?

The value of n can be obtained by using the sine ratio as illustrated below:

Sine θ = Opposite / Hypothenus

Sine 60 = 4√6 / n

√3/2 = 4√6 / n

Cross multiply

n × √3 = 2 × 4√6

n × √3 = 8√6

Divide both side by √3

n = 8√6 / √3

Rationalise

n = 8√6 / √3 × (√3/√3)

n = 8√(6×3) / 3

n = 8√18 / 3

Recall

√18 = √(9×2) = √9 × √2 = 3√2

Thus,

n = 8√18 / 3

n = 8 × 3√2 / 3

n = 8√2

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