Trigonometric Ratios Answers

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Which statements are true for triangle LNM? Check all that apply.

A
The side opposite ∠L is NM.
B
The side opposite ∠N is ML.
C
The hypotenuse is NM.
D
The hypotenuse is LN.
E
The side adjacent ∠L is NM.
F
The side adjacent ∠N is ML.
3

tan(L) =

A
3/5
B
4/3
C
3/4
D
5/4
6

3/53/4✔ 4/55/4

A
3/5
B
3/4
C
4/5
D
5/4
8

✔ RST

A
R
B
S
C
T
9

What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.

A
The length of AC is needed because it is the side adjacent to ∠A.
B
The length of AC is needed because it is the side opposite ∠A.
C
The length of BC is needed because it is the side opposite ∠A.
D
The length of BC is needed because it is the side adjacent to ∠A.
10

3/44/3✔ 4/55/4

A
3/4
B
4/3
C
4/5
D
5/4
11

What is the value of tan(60°)?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

✔ ABC

A
A
B
B
C
C
14

Explain why the value of the sine ratio for an acute angle of a right triangle must always be a positive value less than 1.

Answer:

The sine of an acute angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. In any right triangle, the hypotenuse is the side opposite the 90degree angle, making it the longest side. Because the side opposite an acute angle must be shorter than the hypotenuse, the numerator of the sine ratio is always smaller than the denominator. Therefore, the ratio must be a positive number less than 1.

15

RS✔ T

A
R
B
S
C
T
16

4/55/4✔ 3/55/3

A
4/5
B
5/4
C
3/5
D
5/3
17

✔ ABC

A
A
B
B
C
C
18

What did you include in your response? Check all that apply.

A
The hypotenuse is the longest side.
B
The ratio’s denominator will be larger than the numerator.
C
The larger denominator implies the ratio will be less than 1.
19

3/4✔ 4/34/53/5

A
3/4
B
4/3
C
4/5
D
3/5

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