This section uses the trigonometric ratios to find sides and the hypotenuse of right triangles. A calculator is needed.
The three trigonometric ratios — sine, cosine, and tangent — can be used to find missing side lengths or missing angle measures.
Given right triangle JKL with right angle J, KL = 14 and m ∠ L = 65°. Find JL.
Fill in the blanks.
Step 1: Identify the reference angle, the adjacent leg, the opposite leg, and the hypotenuse.
Mouse over to reveal each term:
Step 2: Identify the information you are given and the information you are looking for.
Step 3: Identify the trigonometric ratio that relates the two side lengths from Step 2.
Step 4: Set up a ratio, including the angle measure, known side length, and unknown side length.
Step 5: Solve for x. Remember that cos (65°) is a number, just like 4, 19, or 0.45. Round to the appropriate place value.
Given right triangle MZQ with right angle M, MZ = 21, and m ∠ Q = 75°
Find ZQ.
Step 1: Identify the reference angle, the adjacent leg, the opposite leg, and the hypotenuse.
Mouse over to reveal each term.
Step 2: Identify the information you are given and the information you are looking for.
Step 3: Identify the trigonometric ratio that relates the two side lengths from Step 2.
Step 4: Set up a ratio, including the angle measure, known side length, and unknown side length
Step 5: Solve for x. Remember that sin (35°) is a number, just like 4, 19, or 0.45. Round to the appropriate place value.