Trigonometric Ratios (Sec 8-2) Answers
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.
3/44/34/55/4
4/55/43/55/3
3/44/34/53/5
X 3/53/44/55/4
RST
What are the angles that make the trigonometric statements true?
ABC
Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal.
What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.
Which statements are true regarding triangle LMN? Check all that apply.
What is the length of side XY? [___]
What is the value of tan(60°)?
Which triangle is similar to △ABC if sin(A) = [image 1] , cos(A) = [image 2] , and tan(A) = [image 3] ?
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 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 90-degree 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.
Sample Response: 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. What did you include in your response? Check all that apply.The hypotenuse is the longest side.The ratio’s denominator will be larger than the numerator.
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