Chapter 10 - NCPN

Lessons 10.5 and 10.6
Review Examples
Find the length, x, of the bridge across
the ravine.
Student Review Exercises
Use the Law of Sines or the Law of
Cosines to find each measure. Round to
the nearest tenth.
Find the missing angle of the triangle.
180º – 108º – 40º = 32º
Apply the Law of Sines.
sin 32° sin 40°
=
18 x
18sin
40°
x =
sin 32°
x ≈ 21.8 yd
Lessons 10.7, 10.8, and 10.9
Review Examples
Find the exact value of cos 105°.
Write 105° as 45° + 60° and use the angle sum
identity cos(A + B) = cos A cos B – sin A sin B.
cos105° =cos 45° • cos60° − sin 45° • sin 60°
=
2 1 2 3
• − •
2 2 2 2
=
2
−
6
4 4
=
2−
6
4
9. Find c if m∠C = 35º, a = 6, and b = 8. 4.6
10. Find m∠B if a = 18, b = 13, and
m∠A = 67º. 41.7º
11. Verify the trigonometric identity
sin θ tan θ =
1
– cos θ.
cos θ
Check students’ work; see margin for sample
12. The lengths of the sides of a triangular
garden are 18 feet, 14 feet, and 10 feet.
What is the measure of the largest angle
of the garden Round to the nearest
tenth. 95.7º
Student Review Exercises
Find the exact value of each expression.
13. tan 105° − 3−2
14. sin 75° 2+
6
4
15. sin 15° 6 − 2
4
16. cos 300° 1 2
Solve each equation.
17. tan 2 θ – tan θ = 0, 0 ≤ θ < 2π 0, ≠ , ≠ ,
5
4
18. sin 2 θ – 1 = 0, 0 ≤ θ < 360° 90°, 270°
≠
4
19. sin 2 θ – 1 = cos 2 θ, 0 ≤ θ < 2π ≠ ,
3 ≠
2
2
Chapter Review 503