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EXAMPLE 3

Find m B by using the Triangle Sum Theorem. 180 o. = 90 o + 42 o + m B. 48 o. = m B. EXAMPLE 3. Solve a right triangle. Solve the right triangle. Round decimal answers to the nearest tenth. SOLUTION. STEP 1. =. BC 70. tan 42 o. 70 tan 42 o. = BC. 70 0.9004.

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EXAMPLE 3

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  1. Find m Bby using the Triangle Sum Theorem. 180o = 90o + 42o + m B 48o = m B EXAMPLE 3 Solve a right triangle Solve the right triangle. Round decimal answers to the nearest tenth. SOLUTION STEP1

  2. = BC70 tan42o 70 tan 42o = BC 70 0.9004 BC BC 63 EXAMPLE 3 Solve a right triangle STEP 2 Approximate BCby using a tangent ratio. Write ratio for tangent of 42o. Multiply each side by 70. Approximate tan. 42o Simplify and round answer.

  3. 70 AB cos42o = ABcos 42o = 70 = AB 70 0.7431 70 cos 42o AB ANSWER 94.2 AB The angle measures are 42o, 48o, and 90o. The side lengths are 70 feet, about 63 feet, and about 94 feet. EXAMPLE 3 Solve a right triangle STEP 3 Approximate ABby using a cosine ratio. Write ratio for cosine of 42o. Multiply each side by AB. Divide each side by cos. 42o Use a calculator to find cos. 42o Simplify .

  4. Suppose your school is building a raked stage. The stage will be 30 feet long from front to back, with a total rise of 2 feet. A rake (angle of elevation) of 5o or less is generally preferred for the safety and comfort of the actors. Is the raked stage you are building within the range suggested? EXAMPLE 4 Solve a real-world problem THEATER DESIGN

  5. sin xo = = 0.0667 2 30 opp. hyp x sin –1 0.0667 3.842 ANSWER The rake is about 3.8o, so it is within the suggested range of 5o or less. EXAMPLE 4 Solve a real-world problem SOLUTION Use the sine and inverse sine ratios to find the degree measure xof the rake.

  6. Find m Xby using the Triangle Sum Theorem. 180o = 90o + 40o + m X 50o = m X for Examples 3, and 4 GUIDED PRACTICE 3. Solve a right triangle that has a 40o angle and a 20 inch hypotenuse. SOLUTION X STEP1 Y Z

  7. = XY20 sin40o 20 sin 40o = XY 20 0.6428 XY BC 12.9 for Examples 3, and 4 GUIDED PRACTICE STEP 2 Approximate YZby using a sine ratio. Write ratio for sine of 40o. Multiply each side by 20. Approximate sin. 40o Simplify and round answer.

  8. YZ 20 = cos40o 20cos 40o = YZ 20 0.7660 YZ YZ 15.3 ANSWER The angle measures are 40o, 50o, and 90o. The side lengths are 12.9 in., about 15.3 in., and 20 in. for Examples 3, and 4 GUIDED PRACTICE STEP 3 Approximate ABby using a cosine ratio. Write ratio for cosine of 40o. Multiply each side by 20. Approximate cos. 40o Simplify and round answer.

  9. sin xo = = 0.1 2 20 opp. hyp ANSWER x sin –1 0.1 5.739 No; the rake is 5.7° so it is slightly larger than the suggested range. for Examples 3, and 4 GUIDED PRACTICE WHAT IF? 4. In Example 4, suppose another raked stage is 20 feet long from front to back with a total rise of 2 feet. Is this raked stage safe? Explain.

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