Understanding 30-60-90 Triangles

Help Questions

Math › Understanding 30-60-90 Triangles

Questions 1 - 2

1

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 $60^\circ$ ?

$7\sqrt{3}$

$14\sqrt{3}$

$7\sqrt{2}$

$\frac{7\sqrt{2}}{2}$

Explanation

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 $7\sqrt{3}$ .

2

Rt_triangle_letters

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

$30^\circ$

$60^\circ$

$45^\circ$

$90^\circ$

Undefined

Explanation

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 $30^\circ$ .

Return to subject