Special right triangles Knowledge-Based Download PDF

Questions

1. 1.

   In right triangle $DEF$, the measure of angle $E$ is $90^\circ$ and the measure of angle $D$ is $45^\circ$. If the area of triangle $DEF$ is $50$, what is the length of hypotenuse $DF$?

   • A) $10$
   • B) $10\sqrt{2}$
   • C) $20$
   • D) $5\sqrt{2}$
2. 2.

   In right triangle $ABC$, the measure of angle $B$ is $90^\circ$, the measure of angle $A$ is $30^\circ$, and the length of hypotenuse $AC$ is $16$. What is the area of triangle $ABC$?

   • A) $16\sqrt{3}$
   • B) $32\sqrt{3}$
   • C) $64\sqrt{3}$
   • D) $64$
3. 3.

   In right triangle $PQR$, the measure of angle $Q$ is $90^\circ$ and the measure of angle $R$ is $60^\circ$. If the length of side $PQ$ is $18$, what is the length of hypotenuse $PR$?

   • A) $6\sqrt{3}$
   • B) $12\sqrt{3}$
   • C) $18\sqrt{3}$
   • D) $36$
4. 4.

   In a right triangle $XYZ$, the measure of angle $Y$ is $90^\circ$ and the measure of angle $X$ is $45^\circ$. If the length of hypotenuse $XZ$ is $14$, what is the length of side $XY$?

   • A) $7$
   • B) $14\sqrt{2}$
   • C) $7\sqrt{2}$
   • D) $\frac{7\sqrt{2}}{2}$
5. 5.

   In a right triangle $ABC$, the measure of angle $C$ is $90^\circ$, the measure of angle $A$ is $30^\circ$, and the length of side $BC$ is $5\sqrt{3}$. What is the length of side $AC$?

   • A) 10
   • B) $10\sqrt{3}$
   • C) 15
   • D) $15\sqrt{3}$