Trigonometric Ratios (sine, Cosine, and Tangent Ratios) Worksheet

**Page 1**

1.

What is the value of sin 45^{o} - cos 45^{o}?

a. | 1 | ||

b. | 2 | ||

c. | 3 |

sin 45

[Substitute the values of sin 45

The value of sin 45

Correct answer : (4)

2.

Round the value of sin 36^{o} to the nearest hundredth.

a. | 0.59 | ||

b. | 0.69 | ||

c. | 0.68 | ||

d. | 0.81 |

[Find using calculator.]

The value of sin 36

[Rounded to nearest hundredth.]

Correct answer : (1)

3.

sin A =

a. | (Side adjacent to A)/Side opposite to A | ||

b. | Hypotenuse/Side opposite to A | ||

c. | (Side opposite to A)/Hypotenuse | ||

d. | (Side opposite to A)/Side adjacent to A |

Correct answer : (3)

4.

What is the value of tan R in the figure?

a. | $\frac{3}{5}$ | ||

b. | $\frac{4}{3}$ | ||

c. | $\frac{3}{4}$ | ||

d. | $\frac{5}{3}$ |

Opposite side of R =

adjacent side of

In ΔABC, tan R =

tan R =

[Substitute the values of PQ and RP.]

Correct answer : (3)

5.

What is the length of side RP in ΔPQR?

a. | 1 foot | ||

b. | 4 feet | ||

c. | 6 feet | ||

d. | 3 feet |

In the figure, RP and PQ are opposite and adjacent sides of angle Q respectively.

tan Q = Opposite side/Adjacent side.

In ΔPQR, tan Q =

tan 45

[Substitute the values of

1 =

[Substitute the value of tan 45

RP = 6

[Simplify.]

The length of side RP is 6 feet.

Correct answer : (3)

6.

What is the length of AC, if the side of each small square is 1 unit?

a. | 6√2 units | ||

b. | 6 units | ||

c. | 8√2 units | ||

d. | 4√2 units |

sin 45

[From the figure.]

From the figure, BC = 4 units

sin 45

[Substitute BC.]

[sin 45

AC = 4√2

[Cross multiply.]

So, the length of AC is 4√2 units.

Correct answer : (4)

7.

a. | 30 ^{o} | ||

b. | 60 ^{o} | ||

c. | 45 ^{o} | ||

d. | 15 ^{o} |

In a right triangle, sin

[Write the formula for the sin ratio.]

=

[Since the opposite side to

=

[Substitute AB = 2 and AC = 4 and simplify.]

= Sin 30

So,

Correct answer : (1)

8.

Find the value of $a$, if ΔABC is a right triangle.

a. | 8.71 | ||

b. | 9.2 | ||

c. | 10 | ||

d. | 6.25 |

[Choose an appropriate trigonometric ratio.]

sin A =

sin 35

[Substitute the values.]

[Multiply each side by

[Divide each side by sin 35

[Simplify.]

[Use table or calculator to find the value of sin 35

[Divide.]

The value of

Correct answer : (1)

9.

A vertical pole is 70 m high. Find the angle formed by the pole at a point 70 m away from its base.

a. | 30 ^{o} | ||

b. | 75 ^{o} | ||

c. | 60 ^{o} | ||

d. | 45 ^{o} |

The height of the pole, AB = 70 m

Let BC be the distance from the base of the pole to the point where the angle is to be measured. So, BC = 70 m

tan C = opposite side/adjacent side

[Choose an appropriate trigonometric ratio.]

From ΔABC, tan C =

tan C =

[Substitute and simplify.]

From the trigonometric tables, tan 45

So, the angle formed by the pole at the point 70 m away from its base is 45

[As tan C = 1 and tan 45

Correct answer : (4)

10.

What is the value of sin A in the figure?

a. | $\frac{12}{13}$ | ||

b. | $\frac{5}{13}$ | ||

c. | $\frac{13}{5}$ | ||

d. | $\frac{13}{12}$ |

In the triangle, BC is the side opposite to A and AC is the hypotenuse.

sin A =

=

[Substitute BC = 5 and AC = 13.]

Correct answer : (2)