PLEASE EXPLAIN BECAUSE A GIRL IS COMPLETELY LOST HERE

Hello!

To find the value of b, we need to use the Law of Sines. The law states,

sin A / a = sin B / b = sin C / c.

We are given these values: sin A = 55 degrees, side a = 8 cm, sin C = 82 degrees.

Since angle B is not given, we have to find it ourselves. We can find the measure of angle B by subtracting both the given angle values from 180 degrees because every triangle is equal to 180 degrees.

180 - 55 - 82 = 43 | The measure of sin B = 43 degrees.

sin (55) / 8 = sin (43) / b (multiply both sides by b)

0.10239... · b = 0.68199... (divide both sides by 0.10239...)

c = 6.6607...

The measure of side b is equal to about 6.7 centimeters.

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Don't be lost. First the triangle angles add to 180 degrees so the angle opposite b, call it B, is

B = 180 - 82 - 55 = 43 degrees

We also have a=8 cm and A=55 degrees

By the Law of Sines

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B}$

$b = \dfrac{a \sin B}{\sin A}$

$b = \dfrac{ 8 \sin 43 }{\sin 55 } \approx 6.7 \textrm{ cm}$

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