Module 7: Practice Problems
1
A=50°, B=70°, a=15. Find b (Law of Sines).
Solution
b=15sin70/sin50 ≈ 18.40.
2
a=10, b=14, C=60°. Find c (Law of Cosines).
Solution
c²=100+196−280cos60=296−140=156. c≈12.49.
3
a=5, b=7, c=10. Find the largest angle.
Solution
cosC=(25+49−100)/70=−26/70. C≈111.8°.
4
Find the area: a=9, b=12, C=45°.
Solution
(1/2)(9)(12)sin45 = 54√2/2 = 27√2 ≈ 38.18.
5
Use Heron's: a=6, b=8, c=10.
Solution
s=12. √[12·6·4·2]=√576=24.
6
A=30°, a=5, b=8. How many triangles (SSA)?
Solution
h=bsinA=8sin30=4. Since h<a<b (4<5<8), two triangles.
7
Find |⟨5, −12⟩|.
Solution
√(25+144)=13.
8
u=⟨3,4⟩, v=⟨−1,2⟩. Find u+v and |u+v|.
Solution
u+v=⟨2,6⟩. |u+v|=√(4+36)=√40=2√10≈6.32.
9
Find the direction angle of ⟨3, 3⟩.
Solution
θ=arctan(3/3)=arctan(1)=45°.
10
Find the unit vector in the direction of ⟨−4, 3⟩.
Solution
|v|=5. Unit=⟨−4/5, 3/5⟩=⟨−0.8, 0.6⟩.