Understanding 30-60-90 Triangles - High School Math

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Question

In this figure, , $Y=6\sqrt{3}$ , and . What is the value of angle ?

Answer

Notice that these sides fit the pattern of a 30:60:90 right triangle: $x:x\sqrt{3}:2x$ .

In this case, .

Since angle is opposite , it must be $30^\circ$ .

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Question

A triangle has angles of $30^\circ:60^\circ:90^\circ$ . If the side opposite the $30^\circ$ angle is , what is the length of the side opposite $60^\circ$ ?

Answer

The pattern for $30^\circ:60^\circ:90^\circ$ is that the sides will be $x:x\sqrt{3}:2x$ .

If the side opposite $30^\circ$ is , then the side opposite $60^\circ$ will be $7\sqrt{3}$ .

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