A triangle is given with one side equal to 18m (a) and angles laying on this side equal to 48∘ (A) and 37∘ (B). Find the ramaining angle (C) and sides (b and c).

∠C=180−∠A−∠B =180−37−48 =95∘ bsin⁡A=asin⁡C bsin⁡37∘=18sin⁡95∘ b=18sin⁡95∘(sin⁡37∘) ≈10.87m csin⁡B=asin⁡C c=18sin⁡95∘(sin⁡48∘) ≈13.43m

"A triangle is given with one side equal..." was answered by our experts

Elleanor Mckenzie

2020-11-24

A triangle is given with one side equal to 18m (a) and angles laying on this side equal to

48^{\circ}

(A) and

37^{\circ}

(B). Find the ramaining angle (C) and sides (b and c).

saiyansruleA

Skilled2020-11-25Added 110 answers

∠ C = 180 - ∠ A - ∠ B

= 180 - 37 - 48

= 95^{\circ}

\frac{b}{\sin A} = \frac{a}{\sin C}

\frac{b}{{\sin 37}^{\circ}} = \frac{18}{{\sin 95}^{\circ}}

b = \frac{18}{{\sin 95}^{\circ}} ({\sin 37}^{\circ})

\approx 10.87 m

\frac{c}{\sin B} = \frac{a}{\sin C}

c = \frac{18}{{\sin 95}^{\circ}} ({\sin 48}^{\circ})

\approx 13.43 m

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