Right Triangles & Trigonometry 1 — Geometry and Trigonometry

Questions in this quiz (7)

1. In a right triangle, the angle opposite side length $$a$$ is $$42°$$. What is the measure of the angle opposite side length $$b$$?

   • $$42°$$
   • $$58°$$
   • $$48°$$
   • $$90°$$

2. In a right triangle, the hypotenuse is $$17$$ and one leg is $$8$$. What is the length of the other leg?

   • $$15$$
   • $$\sqrt{353}$$
   • $$17\sqrt{2}$$
   • $$8\sqrt{2}$$

3. If an equilateral triangle has side lengths of $$14$$, what is the length of an altitude of the equilateral triangle?

   • $$\frac{\sqrt{3}}{2}$$
   • $$7\sqrt{3}$$
   • $$\frac{\sqrt{3}}{3}$$
   • $$\sqrt{3}$$

4. Triangle $$PQR$$ is a $$30-60-90$$ triangle. If $$PR=12$$, $$PQ=k$$ and $$QR=k\sqrt{3}$$. What is the length of $$PQ$$?

   • $$6$$
   • $$12$$
   • $$6\sqrt{3}$$
   • $$24$$

5. Triangle $$PQR$$ is an isosceles right triangle. The length of the hypotenuse $$PR$$ is $$8\sqrt{2}$$. What is the length of $$PQ$$?

   • $$2\sqrt{2}$$
   • $$4\sqrt{2}$$
   • $$8$$
   • $$8\sqrt{2}$$

6. The diagonal of a square is $$12\sqrt{2}$$. What is the length of each side of the square?

   • $$6$$
   • $$6\sqrt{2}$$
   • $$12$$
   • $$12\sqrt{2}$$

7. $$ABC$$ is a right triangle at $$A$$, side $$AC$$ is $$6\sqrt{3}$$, side $$AB$$ is $$6$$, and angle $$ABC$$ is $$60^\circ$$. What is $$\cos(60^\circ)$$ in the right triangle?

   • $$\frac{\sqrt{3}}{3}$$
   • $$\frac{1}{2}$$
   • $$\frac{\sqrt{3}}{2}$$
   • $$\frac{\sqrt{3}}{6}$$