Presentation on theme: "EXAMPLE 3 Solve a right triangle"— Presentation transcript:
1 EXAMPLE 3Solve a right triangleSolve the right triangle. Round decimal answers to the nearest tenth.SOLUTIONSTEP 1Find m B by using the Triangle Sum Theorem.180o= 90o + 42o + m B48o= m B
2 Approximate BC by using a tangent ratio. EXAMPLE 3Solve a right triangleSTEP 2Approximate BC by using a tangent ratio.tan 42o=BC70Write ratio for tangent of 42o.70 tan 42o= BCMultiply each side by 70.BCApproximate tan. 42o63BCSimplify and round answer.
3 Approximate AB by using a cosine ratio. EXAMPLE 3Solve a right triangleSTEP 3Approximate AB by using a cosine ratio.cos 42o=70 ABWrite ratio for cosine of 42o.AB cos 42o=Multiply each side by AB.ABcos 42o=Divide each side by cos. 42oABUse a calculator to find cos. 42oAB94.2Simplify .ANSWERThe angle measures are 42o, 48o, and 90o. The side lengths are 70 feet, about 63 feet, and about 94 feet.
4 EXAMPLE 4Solve a real-world problemTHEATER DESIGNSuppose 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?
5 EXAMPLE 4Solve a real-world problemSOLUTIONUse the sine and inverse sine ratios to find the degree measure x of the rake.sin xo=opp. hyp2 300.0667xsin –ANSWERThe rake is about 3.8o, so it is within the suggested range of 5o or less.
6 GUIDED PRACTICEfor Examples 3, and 43.Solve a right triangle that has a 40o angle and a 20 inch hypotenuse.SOLUTIONXSTEP 1Find m X by using the Triangle Sum Theorem.180o= 90o + 40o + m X50o= m XYZ
7 Approximate YZ by using a sine ratio. GUIDED PRACTICEfor Examples 3, and 4STEP 2Approximate YZ by using a sine ratio.sin 40o=XY20Write ratio for sine of 40o.20 sin 40o= XYMultiply each side by 20.XYApproximate sin. 40o12.9BCSimplify and round answer.
8 Approximate AB by using a cosine ratio. GUIDED PRACTICEfor Examples 3, and 4STEP 3Approximate AB by using a cosine ratio.cos 40o=YZ 20Write ratio for cosine of 40o.20 cos 40o= YZMultiply each side by 20.YZApproximate cos. 40o15.3YZSimplify and round answer.ANSWERThe angle measures are 40o, 50o, and 90o. The side lengths are 12.9 in., about 15.3 in., and 20 in.
9 GUIDED PRACTICEfor Examples 3, and 44.WHAT IF?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.sin xo=opp. hyp2 200.1xsin –No; the rake is 5.7° so it is slightly larger than thesuggested range.ANSWER