Question

In triangle ABC .m/A=35 ,m/B=65 , and c=15. Find b. Round your answer to the nearest tenth. A. 13.8 B. 9.5 C. 8.7 D. 23.7

Answer 1

You would use the Law of Sines here. First realize that if A and B equal 35 and 65 respectively, C=180-65-35=80°. Then from the Law of Sines:

b/sin65=15/sin80

b=15sin65/sin80

b≈13.8 units (to the nearest tenth of a unit)

Answer 2

`\boxed{\boxed{b=13.8}}`

Explanation:

In triangle ABC it is given that,

`m\angle A=35^(\circ),m\angle B=65^(\circ),c=15`

We know that in a triangle sum of all three angle is 180°, so

`\Rightarrow m\angle A+m\angle B+m\angle C=180^(\circ)`

`\Rightarrow m\angle C=180^(\circ)-m\angle A-m\angle B`

`\Rightarrow m\angle C=180^(\circ)-35^(\circ)-65^(\circ)`

`\Rightarrow m\angle C=80^(\circ)`

Applying the Sine law,

`\Rightarrow (\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)`

`\Rightarrow (\sin B)/(b)=(\sin C)/(c)`

`\Rightarrow (\sin 65^(\circ))/(b)=(\sin 80^(\circ))/(15)`

`\Rightarrow (b)/(15)=(\sin 65^(\circ))/(\sin 80^(\circ))`

`\Rightarrow b=(\sin 65^(\circ)* 15)/(\sin 80^(\circ))`

`\Rightarrow b=13.8`