StudentAidUnit 7: Trigonometry — Exercise 7 2
10th Class Mathematics · Unit 7: Trigonometry
7.2.1.(i) Solve the triangle ABC, in which a = 6.1 cm, b = 8.4 cm, α = 42°. (ii) Solve the triangle ABC, in which a = 12.2 cm, c = 15.8 cm, γ = 50°. (iii) Solve the triangle ABC, in which b = 5.2 cm, c = 5 cm, γ = 48°. (iv) Solve the triangle ABC, in which b = 4.8 cm, a = 4 cm, β = 71°. (v) Solve the triangle ABC, in which β = 70°, b = 8 cm, α = 100°. (vi) Solve the triangle ABC, in which a = 6 cm, α = 55°, γ = 60°. (vii) Solve the triangle ABC, in which c = 7 cm, β = 34°, γ = 64°. (viii) Solve the triangle ABC, in which b = 12 cm, α = 92°, β = 77°.
Formula
(i) Sine Rule
asinα=bsinβ=csingamma=k
Working
(i)
k=6.1sin 42^circ=9.116
(i)
sinβ=8.49.116=0.9216 ⇒ β=67.16^circ
(i)
gamma=180^circ-(42^circ+67.16^circ)=70.84^circ
Result
(i)
c=ksingamma=9.116sin 70.84^circ=8.63 cm
Formula
(ii) Sine Rule
asinα=csingamma
Working
(ii)
sinα=12.2sin 50^circ15.8=0.5916 ⇒ α=36.27^circ
(ii)
β=180^circ-(36.27^circ+50^circ)=93.73^circ
Result
(ii)
b=csinβsingamma=15.8sin 93.73^circsin 50^circ=20.58 cm
Formula
(iii) Sine Rule
csingamma=bsinβ
Working
(iii)
sinβ=5.2sin 48^circ5=0.7720 ⇒ β=50.48^circ
(iii)
α=180^circ-(50.48^circ+48^circ)=81.52^circ
Result
(iii)
a=csinαsingamma=5sin 81.52^circsin 48^circ=6.66 cm
Formula
(iv) Sine Rule
asinα=bsinβ
Working
(iv)
sinα=4sin 71^circ4.8=0.7879 ⇒ α=51.87^circ
(iv)
gamma=180^circ-(51.87^circ+71^circ)=57.13^circ
(iv)
c=asingammasinα=4.27 cm
Result
(iv) Answer (as printed)
α=81.52^circ, gamma=57.13^circ, c=4.27 cm
α was computed correctly as 51.87° in the working line above, but the boxed answer prints 81.52° instead (apparently copied from part (iii)'s α value). γ and c are correct.
(v)
gamma=180^circ-(100^circ+70^circ)=10^circ
Working
(v)
a=bsinαsinβ=8sin 100^circsin 70^circ=8.38 cm
Result
(v)
c=bsingammasinβ=8sin 10^circsin 70^circ=1.48 cm
(vi)
β=180^circ-(55^circ+60^circ)=65^circ
Working
(vi)
b=asinβsinα=6sin 65^circsin 55^circ=6.64 cm
Result
(vi)
c=asingammasinα=6sin 60^circsin 55^circ=6.34 cm
(vii)
α=180^circ-(34^circ+64^circ)=82^circ
Working
(vii)
a=csinαsingamma=7sin 82^circsin 64^circ=7.71 cm
Result
(vii)
b=csinβsingamma=7sin 34^circsin 64^circ=4.35 cm
(viii)
gamma=180^circ-(92^circ+77^circ)=11^circ
Working
(viii)
a=bsinαsinβ=12sin 92^circsin 77^circ=12.30 cm
Result
(viii)
c=bsingammasinβ=12sin 11^circsin 77^circ=2.35 cm
7.2.2.(i) Calculate the area of triangle ABC, in which a = 7 cm, b = 8 cm, γ = 38°. (ii) Calculate the area of triangle ABC, in which a = 11 cm, c = 14 cm, β = 51°. (iii) Calculate the area of triangle ABC, in which b = 3 cm, c = 9 cm, α = 78°. (iv) Calculate the area of triangle ABC, in which a = 10 cm, α = 62°, β = 69°. (v) Calculate the area of triangle ABC, in which c = 4 cm, β = 36°, γ = 80°. (vi) Calculate the area of triangle ABC, in which c = 6.6 cm, α = 23°, γ = 89°. (vii) Calculate the area of triangle ABC, in which a = 5.3 cm, b = 4.7 cm, c = 8.2 cm. (viii) Calculate the area of triangle ABC, in which a = 6.12 cm, b = 8.34 cm, c = 7.12 cm.