Download Solving Right Triangles

Analytic Geometry
Name: _________________________
Solving Right Triangles
Date: ___________
1. To solve a right triangle means to find the measures of all of its ______________ and all
of its ______________.
Use a calculator to approximate the measure of A to the nearest tenth of a degree.
2.
3.
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5.
6.
7.
Solve the right triangles. Round angle measures to the nearest tenth and the side lengths
to the nearest hundredth.
8.
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17. Use the triangle to the right to find:
a) Perimeter of the triangle
b) Area of the triangle
18. Given the triangle to the right, find:
a) sin 
b) tan 
c) cos C
15
5

5
15
C
19. Use the given right triangle. Label one of the acute angles
as 71º. Then mark the correct sides as 3 and 5 showing
5
that the tan 71º = .
3
20. Use your calculator to compare the following:
Complementary angles are two angles whose sum is _________.
a) sin 50º and cos 40º
b) sin 20º and cos 70º
c) sin 25º and cos 65º
d) sin 5º and cos 85º
e) sin 10º and cos 80º
f) sin 48º and cos 42º
Looking at the results above. What conclusion can you state about the relationship between sine
and cosine for two complementary angles?
Answers: Solving Right Triangles
1. side lengths & angle measures
2. mA = 33.7o
3. mA = 54.3o
4. mA = 74.1o
5. mA = 27.0o
6. mA = 24.4o
7. mA = 53.1o
8. KL ≈ 5.14, ML ≈ 6.13, mK = 50o
9. NP ≈ 21.45, NQ ≈ 23.66, mN = 25o
10. RS ≈ 9.74, RT ≈ 17.89, mT = 33o
11. AC = 15, mA ≈ 36.9, mC ≈ 53.1
12. EF ≈ 8.49, mF ≈ 19.5, mD ≈ 70.5
13. HJ ≈ 7.75, mJ ≈ 61.0o, mG ≈ 29.0o
14. AC ≈ 4.95, AB ≈ 7.18, mA = 46.4o
15. ED ≈ 5.37, mD ≈ 29.7o, mE ≈ 60.3o
16. JH ≈ 5.42, JG = 9.43, mH = 60.1o
17. a) 20 + 10√2; b) 25√2
18. a)
2 2
2 2
; b) 2 2 ; c)
3
3
71
3
5
19.
20. they’re equal!