Free Printable Similarity and Trigonometric Ratio

1.

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

a)

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

b)

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

c)

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

d)

$\tan60=\frac{h}{1000}$

2.

What is the correct equation to solve for x ?

a)

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

b)

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

c)

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

d)

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

3.

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

a)

A and H

b)

O and H

c)

O and A

d)

H and shortside

4.

Find the value of x. Round to the nearest tenth.

(a)

5.

adjacent ÷ hypotenuse =

a)

sin

b)

cos

c)

tan

d)

trigonometry

6.

opposite ÷ adjacent =

a)

sin

b)

cos

c)

tan

d)

trigonometry

7.

Which of the following statements are true? 2 answers

a)

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

b)

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

c)

$\tan60=\frac{a}{7}$

d)

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

e)

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

8.

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

a)

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

b)

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

c)

$x=\tan\left(\frac{33}{56}\right)$

d)

$x=\tan\left(\frac{56}{33}\right)$

9.

For an acute angle 𝜃, the equation sin(𝜃) = cos(13) is true. What is the value of 𝜃?

(a)

10.

Which theorem proves that these triangles are similar?

a)

Angle-Angle Similarity Theorem

b)

Side-Angle-Side Similarity Theorem

c)

Side-Side-Side Similarity Theorem

d)

Right Triangle Similarity Theorem

11.

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

a)

$\frac{q}{r}$

b)

$\frac{x}{y}$

c)

$\frac{s}{r}$

d)

$\frac{q}{s}$

12.

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

a)

$\frac{x}{z}$

b)

$\frac{y}{z}$

c)

$\frac{q}{s}$

d)

$\frac{r}{s}$

13.

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.

a)

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

b)

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

c)

Corresponding angles of similar triangles are congruent.

d)

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

14.

If $\frac{y}{z}=0.6$ , then what is the measure of $\alpha$ ? Round your answer to the nearest tenth.

(a)

15.

opposite ÷ hypotenuse =

a)

sin

b)

cos

c)

tan

d)

trigonometry

Similarity and Trigonometric Ratio

Total questions: 15

Worksheet time: 15mins

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