ANSWER 8.0 ANSWER 11.3 2. If m P = 58° and r = 5, find p. 1. If PR = 12 and m R = 19°, find p. Use...
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Transcript of ANSWER 8.0 ANSWER 11.3 2. If m P = 58° and r = 5, find p. 1. If PR = 12 and m R = 19°, find p. Use...
![Page 1: ANSWER 8.0 ANSWER 11.3 2. If m P = 58° and r = 5, find p. 1. If PR = 12 and m R = 19°, find p. Use this diagram for Exercises 1–4. 4. If r = 8 and p =](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e895503460f94b8ea45/html5/thumbnails/1.jpg)
ANSWER 8.0
ANSWER 11.3
2. If m P = 58° and r = 5, find p.
1. If PR = 12 and m R = 19°, find p.
Use this diagram for Exercises 1–4.
4. If r = 8 and p = 12, find q.
14.4
10.4
3. If m P = 60°, and p = 9 , find q.
![Page 2: ANSWER 8.0 ANSWER 11.3 2. If m P = 58° and r = 5, find p. 1. If PR = 12 and m R = 19°, find p. Use this diagram for Exercises 1–4. 4. If r = 8 and p =](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e895503460f94b8ea45/html5/thumbnails/2.jpg)
Solve Right Triangles
5.4 (M2)
![Page 3: ANSWER 8.0 ANSWER 11.3 2. If m P = 58° and r = 5, find p. 1. If PR = 12 and m R = 19°, find p. Use this diagram for Exercises 1–4. 4. If r = 8 and p =](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e895503460f94b8ea45/html5/thumbnails/3.jpg)
Vocabulary “To solve a right triangle” means to find the
measures of all of its sides and angles. Inverse Tangent:
C
B
A
1tanBC
m AAC
1tan , tanIf A x then x m A
![Page 4: ANSWER 8.0 ANSWER 11.3 2. If m P = 58° and r = 5, find p. 1. If PR = 12 and m R = 19°, find p. Use this diagram for Exercises 1–4. 4. If r = 8 and p =](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e895503460f94b8ea45/html5/thumbnails/4.jpg)
C
B
A
1sinBC
m AAB
1sin , sinIf A y then y m A
1cosAC
m AAB
1cos , cosIf A z then z m A
Inverse Trigonometry
![Page 5: ANSWER 8.0 ANSWER 11.3 2. If m P = 58° and r = 5, find p. 1. If PR = 12 and m R = 19°, find p. Use this diagram for Exercises 1–4. 4. If r = 8 and p =](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e895503460f94b8ea45/html5/thumbnails/5.jpg)
EXAMPLE 1 Use an inverse tangent to find an angle measure
Use a calculator to approximate the measure of A to the nearest tenth of a degree.
SOLUTION
Because tan A =
1520
34
= = 0.75, tan–1 0.75 = m A
Use a calculator.
tan –1 0.75 36.86989765. . .
ANSWER
So, the measure of A is approximately 36.9o.
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EXAMPLE 2 Use an inverse sine and an inverse cosine
Let 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 = 0.87 b. cos B = 0.15
SOLUTION
a. m A = sin –1 0.87 60.5o
b. m B = cos –1 0.15 81.4o
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GUIDED PRACTICE for Examples 1 and 2
1. Look back at Example 1. Use a calculator and an inverse tangent to approximate m C to the nearest tenth of a degree.
ANSWER 53.1o
2. Find m D to the nearest tenth of a degree if sin D = 0.54.
ANSWER 32.7o
![Page 8: ANSWER 8.0 ANSWER 11.3 2. If m P = 58° and r = 5, find p. 1. If PR = 12 and m R = 19°, find p. Use this diagram for Exercises 1–4. 4. If r = 8 and p =](https://reader036.fdocuments.in/reader036/viewer/2022062718/56649e895503460f94b8ea45/html5/thumbnails/8.jpg)
EXAMPLE 3 Solve a right triangle
Solve the right triangle. Round decimal answers to the nearest tenth.
SOLUTION
STEP 1
Find m B by using the Triangle Sum Theorem.
180o = 90o + 42o + m B48o = m B
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EXAMPLE 3 Solve a right triangle
STEP 2
Approximate BC by using a tangent ratio.
tan 42o =BC70
Write ratio for tangent of 42o.
70 tan 42o = BC Multiply each side by 70.
Approximate tan 42o70 0.9004 BC
63 BC Simplify and round answer.
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EXAMPLE 3 Solve a right triangle
STEP 3
Approximate AB by using a cosine ratio.
cos 42o =70 AB
Write ratio for cosine of 42o.
AB cos 42o = 70 Multiply each side by AB.
Divide each side by cos 42o.
Use a calculator to find cos 42o.
AB 70 cos 42o=
AB 70 0.7431
AB 94.2 Simplify .
ANSWER The angle measures are 42o, 48o, and 90o. The
side lengths are 70 feet, about 63 feet, and about 94 feet.
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EXAMPLE 4 Solve a real-world problem
THEATER DESIGN
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?
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EXAMPLE 4 Solve a real-world problem
SOLUTION
Use the sine and inverse sine ratios to find the degree measure x of the rake.
sin xo =opp. hyp
= 2 30
0.0667
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.
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GUIDED PRACTICE for Examples 3 and 4
3. Solve a right triangle that has a 40o angle and a 20 inch hypotenuse.
ANSWER
40o, 50o, and 90o, about 12.9 in., about 15.3 in. and 20 in.