Right Triangles & Trigonometry 2 — Geometry and Trigonometry

Questions in this quiz (7)

1. In the right triangle $$ABC$$, right at A. Angle $$B=45^\circ$$, angle $$C=45^\circ$$, and the hypotenuse $$BC=10$$. What is $$\sin(45^\circ)$$ in the triangle?

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

2. In the right triangle $$ABC$$, right at $$A$$. Angle $$B=45^\circ$$, angle $$C=45^\circ$$, and the hypotenuse $$BC=10$$. What is $$\tan(45^\circ)$$ in the triangle?

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

3. Triangle $$ABC$$ is right at $$A$$ , angle $$B$$ measures $$\frac{\pi}{4}$$. The hypotenuse has length $$1$$, and the leg adjacent to angle $$B$$ has length $$\frac{\sqrt{2}}{2}$$. What is $$\sin\left(\frac{\pi}{4}\right)$$ in the triangle?

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

4. What is $$\sin(30^\circ)$$?

   • $$\frac{1}{4}$$
   • $$\frac{\sqrt{2}}{2}$$
   • $$\frac{1}{2}$$
   • $$\frac{\sqrt{3}}{2}$$

5. What other sine value on the unit circle is equivalent to $$\sin(60^\circ)$$?

   • $$\sin(120^\circ)$$
   • $$\sin(30^\circ)$$
   • $$\sin(90^\circ)$$
   • $$\sin(160^\circ)$$

6. In the above right triangle, if $$\sin(a^\circ)=0.6$$, what is $$\cos(b^\circ)$$?

   • $$0.4$$
   • $$0.6$$
   • $$0.8$$
   • $$1$$

7. If $$cosY=\frac{\sqrt{3}}{2}$$ and angle $$Y$$ is between $$0^{\circ}$$ and $$90^{\circ}$$ what is the degree measure of angle $$Y$$?

   • $$30^{\circ}$$
   • $$45^{\circ}$$
   • $$60^{\circ}$$
   • $$90^{\circ}$$