GP4-­‐HW9 PAP Precalculus Chapter 9.2 – Law of Sines Solution 180! = 45! + 95! + 𝐴 𝐴 = 40! sin 95! sin 45!
=
5
𝑏
5 sin 45!
𝑏=
sin 95!
𝑏 ≈ 3.55 sin 95! sin 40!
=
5
𝑎
5 sin 40!
𝑎=
sin 95!
𝑎 ≈ 3.23 Solution ℎ = 3 sin 40! ≈ 1.93 Since ℎ < 𝑏 < 𝑐, there are two possible triangles Triangle 1 sin 40! sin 𝐶
=
2
3
3 sin 40!
!!
𝐶 = sin
≈ 74.6! 2
180! = 𝐴 + 40! + 74.6! 𝐴 = 65.4! sin 40! sin 65.4!
=
2
𝑎
2 sin 65.4
𝑎=
≈ 2.83 sin 40!
Triangle 2 sin 40! sin 𝐶
=
2
3
3 sin 40!
𝐶 = sin!!
≈ 74.6! , or 105.4! 2
180! = 𝐴 + 40! + 105.4! 𝐴 = 34.6! sin 40! sin 34.6! =
2
𝑎
2 sin 34.6!
𝑎=
≈ 1.77 sin 40!
ℎ = 31 sin 85! ≈ 30.88 𝑎 = 30 cm is not long enough to form a triangle. 𝑐 > 𝑏, so only one triangle can be formed. ℎ = 31 sin 29! ≈ 15.03 ℎ < 𝑏 < 𝑎, so two triangles can be formed.