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

Answer:

$\boxed{\boxed{b=13.8}}$

Step-by-step 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,

$\Rightarrow \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

$\Rightarrow \dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

$\Rightarrow \dfrac{\sin 65^{\circ}}{b}=\dfrac{\sin 80^{\circ}}{15}$

$\Rightarrow \dfrac{b}{15}=\dfrac{\sin 65^{\circ}}{\sin 80^{\circ}}$

$\Rightarrow b=\dfrac{\sin 65^{\circ}\times 15}{\sin 80^{\circ}}$

$\Rightarrow b=13.8$

Answer 2

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)