Question

Find b, given that a=20, angle A= 30 degrees, and angle B= 45 degrees in triangle ABC

Answer 1

Step-by-step explanation:

This can be solved by many ways :-

1) Using the Sine Rule of triangles :-

The Sine rule states that :-

a / Sin A  =  b / Sin B  =  c / Sin C

∴  a / Sin A  =  b / Sin B

∴ 20 / Sin 30°  =  b / Sin 45°

∴ 20 / (1/2)  =  b / (1 / √2)

∴ 40  =  √2 × b

∴ b  =  40 / √2  =  20√2.

∴ b  =  20√2

# If you want the solution in any other method please comment. I would be glad to help you !!!

Answer 2

Hello!

Find b, given that a=20, angle A= 30 degrees, and angle B= 45 degrees in triangle ABC

• The side b is opposite to the angle B, applying the law of the sines, we have:

$\dfrac{a}{sinA} = \dfrac{b}{sinB}$

$\dfrac{20}{sin30^0} = \dfrac{b}{sin45^0}$

$\dfrac{20}{ \dfrac{1}{2} } = \dfrac{b}{ \dfrac{ \sqrt{2} }{2} }$

 

$20* \dfrac{ \sqrt{2} }{2} = b* \dfrac{1}{2}$

$\dfrac{20 \sqrt{2} }{2} = \dfrac{b}{2}$

$2*b =2*20 \sqrt{2}$

 

$2\:b = 40 \sqrt{2}$

 

$b = \dfrac{40 \sqrt{2} }{2}$

 

$\boxed{\boxed{b = 20 \sqrt{2} }}\:\:\:\:\:\:\bf\green{\checkmark}$

Answer:

b = 20√2

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