Trigonometric Ratios Assignment

Use the diagram of triangle XYZ to answer the questions. What is the length of side XY? What is the value of sin(X)? What is the value of cos(X)? What is the value of tan(X)?

10 4/5 3/5 4/3

What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain. The length of AC is needed because it is the side adjacent to ∠A. The length of AC is needed because it is the side opposite ∠A. The length of BC is needed because it is the side opposite ∠A. The length of BC is needed because it is the side adjacent to ∠A.

C. The length of BC is needed because it is the side opposite ∠A.

What is the value of tan(60°)?

/3

What are the angles that make the trigonometric statements true? sin( ) = cos(B) sin(B) = cos( )

A, A

What are the values of the three trigonometric ratios for angle L, in simplest form? sin(L) = cos(L) = tan(L) =

4/5 3/5 4/3

Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal.

B

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.

The sine ratio is the length of the side opposite a given acute angle divided by the length of the hypotenuse. Because the hypotenuse is the side opposite the largest angle, the 90° angle, it has to be the longest side. Thus, the ratio will have a denominator that is larger than the numerator, and the ratio will be less than 1.

Which triangle is similar to △ABC if sin(A) = , cos(A) = , and tan(A) = ?

B

Consider △LNM. Which statements are true for triangle LNM? Check all that apply. The side opposite ∠L is NM. The side opposite ∠N is ML. The hypotenuse is NM. The hypotenuse is LN. The side adjacent ∠L is NM. The side adjacent ∠N is ML.

The side opposite ∠L is NM The side opposite ∠N is ML The hypotenuse is LN.

Which statements are true regarding triangle LMN? Check all that apply. NM = x NM = x/2 LM = x/2 tan(45°) = /2/2 tan(45°) = 1

NM = x LM = x/2 tan(45) = 1

Use the diagram and side lengths of triangle RST to determine the angles used for the trigonometric ratios. sin( ) = 12/13 tan( ) = 5/12

R T