Special right triangles Knowledge-Based Practice

Questions

1. 1.

   In right triangle $ABC$, $\angle C = 90^\circ$ and $\angle A = 30^\circ$. If the length of the median drawn from vertex $C$ to the hypotenuse $AB$ is $8$, what is the length of leg $AC$?

   • A) $8$
   • B) $4\sqrt{3}$
   • C) $8\sqrt{3}$
   • D) $16\sqrt{3}$
2. 2.

   In triangle $ABC$, $\angle A = 30^\circ$, $\angle B = 45^\circ$, and side $BC = 6\sqrt{2}$. What is the length of side $AC$?

   • A) $6\sqrt{3}$
   • B) $6\sqrt{6}$
   • C) $12$
   • D) $12\sqrt{2}$
3. 3.

   In a $30^\circ\text{–}60^\circ\text{–}90^\circ$ special right triangle, the perimeter is $12 + 4\sqrt{3}$. What is the length of the hypotenuse?

   • A) 4
   • B) $4\sqrt{3}$
   • C) 8
   • D) $8\sqrt{3}$

Answers and step-by-step solutions appear after you finish the test.