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Sunny_sXe [5.5K]
3 years ago
8

Using the 60-30-90 right triangle method, find x and answer in simplest radical form.

Mathematics
1 answer:
wariber [46]3 years ago
8 0

Answer:

x = 2 \sqrt{10}

Step-by-step explanation:

Since the triangle is right we can use the sine ratio to find x

sin60° = \frac{opposite}{hypotenuse} = \frac{\sqrt{30} }{x}

[ note the exact value of sin60° = \frac{\sqrt{3} }{2} ], hence

\frac{\sqrt{3} }{2} = \frac{30}{x}

multiply both sides by 2x, hence

\sqrt{3} x = 2\sqrt{30}

divide both sides by \sqrt{3}

x = \frac{2\sqrt{30} }{\sqrt{3} } = 2\sqrt{\frac{30}{3} } = 2\sqrt{10}


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