Consider the non-right triangle below Suppose that m∠ACB=103∘ and m∠BAC=44∘, and that y=50.5cm. What is the value of x?

Step 1 We know that the sum of angles in a triangle equals 180∘ degrees. Therefore, ∠BAC+∠CBA+∠ACB=180∘ ∠CBA=180∘−∠BAC−∠ACB ∠CBA=180∘−44∘−103∘ ∠CBA=33∘ Step 2 By using law of sines in the given triangle, sin⁡∠BACx=sin⁡∠CBAy sin⁡44∘x=sin⁡33∘50.5 x=sin⁡44∘sin⁡33∘×50.5 x=0.69460.5446×50.5 x=64.41 The value of x is therefore 64.41 cm

"Consider the non-right triangle below Suppose that m∠ACB=103∘..." was answered by our community

High School
Geometry
Trigonometry
Non-right triangles and trigonometry

embaseclielenzn

Answered question

2021-11-22

Consider the non-right triangle below

Suppose that

m ∠ A C B = 103^{\circ}

and

m ∠ B A C = 44^{\circ}

, and that

y = 50.5 c m

. What is the value of x?

Answer & Explanation

Sue Leahy

Beginner2021-11-23Added 13 answers

Step 1
We know that the sum of angles in a triangle equals

180^{\circ}

degrees. Therefore,

∠ B A C + ∠ C B A + ∠ A C B = 180^{\circ}

∠ C B A = 180^{\circ} - ∠ B A C - ∠ A C B

∠ C B A = 180^{\circ} - 44^{\circ} - 103^{\circ}

∠ C B A = 33^{\circ}

Step 2
By using law of sines in the given triangle,

\frac{\sin ∠ B A C}{x} = \frac{\sin ∠ C B A}{y}

\frac{{\sin 44}^{\circ}}{x} = \frac{{\sin 33}^{\circ}}{50.5}

x = \frac{{\sin 44}^{\circ}}{{\sin 33}^{\circ}} \times 50.5

x = \frac{0.6946}{0.5446} \times 50.5

x = 64.41

The value of x is therefore 64.41 cm

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Trigonometry

Didn't find what you were looking for?