Download Answers for the lesson “Solve Right Triangles”

LESSON
7.7
Answers for the lesson “Solve Right
Triangles”
Skill Practice
20. To determine the measure of
angle T using cosine, the ratio is
adjacent over hypotenuse;
1. angles, sides
2. Use the Pythagorean Theorem if
15
5 mŽT.
cos21 }
you have two sides of the triangle.
17
Use a trigonometric ratio if you
21. 308
22. 48.68
have an angle measure and a
side length.
24. 50.28 25. 458
26. 15.68
3. 33.78
4. 24.48
5. 74.18
27. 11.08
6. 27.08
7. 53.18
8. 54.38
30. tan21 is the function which is
9. B
10. mŽK 5 508, KL ø 5.1, ML ø 6.1
11. mŽN 5 258, NP ø 21.4,
NQ ø 23.7
12. mŽT 5 338, RS ø 9.7, RT ø 17.9
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
23. 70.78
13. mŽA ø 36.98, mŽB ø 53.18,
AC ø 15
14. mŽD ø 70.58, mŽF ø 19.58,
EF ø 8.5
28. 35.98
29. B
used to determine the measure
of an angle given the proper ratio
of sides.
31. 458; 608
32. a. 0 to 108
b. 898
c. 608
d. no
}
33. 6 cm, 2 cm, 2Ï 10 cm, 908,
about 18.48, about 71.68
Problem Solving
15. mŽG ø 298, mŽ J ø 618,
34. about 38.78
16. mŽA 5 46.48, AB ø 7.2,
12
35. about 59.78; tan21 } ø 59.78
7
HJ ø 7.7
AC ø 5.0
36. no
17. mŽD ø 29.78, mŽE ø 60.38,
ED ø 5.4
18. mŽH 5 60.18, GJ ø 9.4,
JH ø 5.4
19. WX should have been used instead
7
5 368.
of WY; sin21 }
WX
BC
37. tan21 }; the information
AC
needed to determine the measure
of A is given. If you used the
tangent ratio, this will make the
answer more accurate since no
rounding has occurred.
Geometry
Answer Transparencies for Checking Homework
219
38. a. about 1716 ft
40. Sample answer: You want to
b. about 2986 ft
c. About 1270 ft; subtract the
two distances to find out how
far the two hikers are from each
other.
39. a.
41. a. 38.4 ft
b. about 71.2 ft
x (inches)
20
21
22
y (degrees) 28.8 27.6 26.6
x (inches)
23
24
25
y (degrees) 25.6 24.6 23.7
x (inches)
26
27
y (degrees) 22.9 22.2
c. about 48.7 ft
d. about 57.48, about 38.08;
neither; the sides are not the
same, so the triangles are not
congruent, and the angles are
not the same, so the triangles
are not similar.
e. Tangent was used because the
b.
y
30
Degrees
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
know how tall your town’s water
tower is. You are standing 40 feet
away from the base of the tower
and the angle of elevation is 608.
How tall is the water tower?
42. Statements (Reasons)
20
1. nABC with altitude }
CD
(Given)
10
0
height and the distance along
the ground form a tangent
relationship for the angle
of elevation.
0 20 21 22 23 24 25 26 27 28 x
Inches
CD
CD
and sin B 5 }
2. sin A 5 }
a
b
(Definition of sine)
c. Sample answer: The longer
the rack, the closer to 208 the
angle gets.
3. CD 5 b sin A and
CD 5 a sin B
(Multiplication Property
of Equality)
Geometry
Answer Transparencies for Checking Homework
220
4. b sin A 5 a sin B
(Substitution Property
of Equality)
sin A
sin B
5}
5. }
b
a
4. about 18.9 ft;
1
8
.
9
(Division
Property of Equality)
Mixed Review of
Problem Solving
1. a. about 13.0 m
b. about 17.8 m
c. about 4.8 m
}
2. a. friend10 myou
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
85
5. a. 9Ï 3 . Sample answer: Use the
Pythagorean Theorem with
n AEC, since n ACD is
} is bisected by
isosceles, and AD
E, }
EC is the altitude and is
therefore perpendicular to
the base.
b. About 10.98. Sample answer:
rock
b. Use the tangent ratio.
Find the measure of Ž ACE
using the sine ratio, then find
the measure of Ž ACB because
it is supplementary to Ž ACE.
The Law of Cosines allowed
me to find AB and then I used
the Law of Sines to find the
measure of Ž ABC.
c. about 76.5 m
1.35
3. about 2.4 m; sin 348 5 }
x
Geometry
Answer Transparencies for Checking Homework
221
5. c. Sample answer: Part (a): Since
the hypotenuse is 18 and the
given leg is half of that, the
triangle must be a 308-608-908
triangle and therefore, the other
}
leg must be 9Ï 3 ; part (b): EB
must equal 3x and since
}
}
x 5 9Ï 3 , EB 5 27 Ï3 . Now
you can use the inverse tangent
function to determine the
measure of Ž ABC.
6. about 8.6 ft; about 11.0 ft
7. 658;
5
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
6
Geometry
Answer Transparencies for Checking Homework
222