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31 votes
Can you find both the value of x and y? It is a 30-60-90 triangle

Can you find both the value of x and y? It is a 30-60-90 triangle-example-1
User Aditi
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1 Answer

17 votes
17 votes

Answer:

x = 8*root3

y = 16

Explanation:

You can use tangent and cosine of 60° to find x and y, BUT THERE'S A SHORTCUT. You pointed out that its a 30°-60°-90° triangle. That is a special right triangle. Here's the shortcut:

the longest side (hypotenuse) is double the shortest side. We have an 8 on the shortest side, so the hypotenuse (longest side) is 16. This ALWAYS works for 30°-60°-90° triangles!

Another shortcut:

The longer leg is the shorter leg × root3.

This ALWAYS works on 30°-60°-90° triangles.

So on your triangle, the short side is 8, that means the longer leg is 8×root3.

ta-daaaa!

User Abbey Graebner
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2.8k points