Presentation on theme: "Use this diagram for Exercises 1–4."— Presentation transcript:
1 Use this diagram for Exercises 1–4. 1. If PR = 12 and m R = 19°, find p.ANSWER11.32. If m P = 58° and r = 5, find p.ANSWER8.03. If m P = 60°, and p = 9 , find q.10.44. If r = 8 and p = 12, find q.14.4
5 EXAMPLE 1Use an inverse tangent to find an angle measureUse a calculator to approximate the measure of A to the nearest tenth of a degree.SOLUTIONBecause tan A =152034== 0.75,tan–1 0.75= m AUse a calculator.tan –ANSWERSo, the measure of A is approximately 36.9o.
6 EXAMPLE 2Use an inverse sine and an inverse cosineLet A and B be acute angles in a right triangle. Use a calculator to approximate the measures of A and B to the nearest tenth of a degree.a.sin A = 0.87b.cos B = 0.15SOLUTIONa.m A= sin –1 0.8760.5ob.m B= cos –81.4o
7 GUIDED PRACTICEfor Examples 1 and 21.Look back at Example 1. Use a calculator and an inverse tangent to approximate m C to the nearest tenth of a degree.ANSWER53.1o2.Find m D to the nearest tenth of a degree if sin D = 0.54.ANSWER32.7o
8 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
9 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.
10 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 42o.ABUse a calculator to find cos 42o.AB94.2Simplify .ANSWERThe angle measures are 42o, 48o, and 90o. Theside lengths are 70 feet, about 63 feet, and about 94 feet.
11 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?
12 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.
13 GUIDED PRACTICEfor Examples 3 and 43.Solve a right triangle that has a 40o angle and a 20 inch hypotenuse.ANSWER40o, 50o, and 90o, about 12.9 in., about 15.3 in. and 20 in.