Quiz about Similarity and Trigonometric Ratio

Question 1

Which trigonometric ratio you should use to find the height(h)?

Accepted Answer

$$\cos60=\frac{h}{1000}$$

Answer

$$\sin60=\frac{h}{1000}$$

Answer

$$\cos60=\frac{1000}{h}$$

Answer

$$ an60=\frac{h}{1000}$$

Question 2

What is the correct equation to solve for x ?

Accepted Answer

$$ an(58)=\frac{11}{x}$$

Answer

$$\cos(58)=\frac{x}{11}$$

Answer

$$\sin(58)=\frac{x}{11}$$

Answer

$$\sin(58)=\frac{11}{x}$$

Question 3

What two side lengths are being used in this right-angle triangle?

Accepted Answer

O and A

Answer

A and H

Answer

O and H

Answer

H and shortside

Question 4

Which of the following statements are true? 2 answers

Accepted Answer

$$\sin30=\frac{7}{c}$$

Accepted Answer

$$\cos60=\frac{7}{c}$$

Answer

$$\sin30=\frac{a}{c}$$

Answer

$$ an60=\frac{a}{7}$$

Answer

$$\cos60=\frac{a}{c}$$

Question 5

Which equation can you use to find the value of t?

Accepted Answer

$$ an t=\frac{33}{56}$$

Answer

$$ an t=\frac{56}{33}$$

Answer

$$x= an\left(\frac{33}{56} ight)$$

Answer

$$x= an\left(\frac{56}{33} ight)$$

Question 6

Which theorem proves that these triangles are similar?

Accepted Answer

Angle-Angle Similarity Theorem

Answer

Side-Angle-Side Similarity Theorem

Answer

Side-Side-Side Similarity Theorem

Answer

Right Triangle Similarity Theorem

Question 7

Which ratio is equivalent to $$\frac{z}{y}$$ ?

Accepted Answer

$$\frac{s}{r}$$

Answer

$$\frac{q}{r}$$

Answer

$$\frac{x}{y}$$

Answer

$$\frac{q}{s}$$

Question 8

Which ratios of side lengths are equal to $$\cos\left(\alpha\right)$$ ?

Accepted Answer

$$\frac{x}{z}$$

Accepted Answer

$$\frac{q}{s}$$

Answer

$$\frac{y}{z}$$

Answer

$$\frac{r}{s}$$

Question 9

Explain why the values of the trigonometric ratios only depend on the angle $$\alpha$$ and not on the particular lengths x, y, z, q, r, s.

Accepted Answer

The triangles are similar, so ratios like $$\frac{opposite}{hypotenuse}$$ will be the same.

Accepted Answer

Side lengths of similar triangles are proportional, so ratios of corresponding side lengths will be equal.

Answer

Corresponding angles of similar triangles are congruent.

Answer

The side lengths of similar triangles can be different, but the angles will be the same.

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