Question

Can someone please explain to me how they got 44 degrees??

Answer 1

Sine rule states that the ratio of a side of a triangle to the angle opposite the side is equivalent for all 3 sides and their respective opposite angles.

`\boxed{ (sinA)/(a) = (sinB)/(b) = (sinC)/(c) }`

Thus, the side opposite ∠B is side AC, which is 10 units long. The side opposite ∠A is side BC, which is 8 units long. Substitute these values into the formula. (We are at line 2 of working)

Line 3: multiply both sides by 10 to find sinB

This would give us

`sinB = (10sin34°)/(8)`

This is can also be written as: (as seen in line 4)

`sinB = (10)/(8)( sin34°)`

To find the measure of angle B:

`m∠B = sin^( - 1) ( (10sin34°)/(8) ) \\ m∠B = 44° \\ (nearest \: degree)`

~ Explanation for line 6 and onwards~

The sine of an angle is positive in quadrants I and II. Since sinB is positive (≈0.69899), we are looking at these 2 quadrants. Since the reference angle is 44° rounded off to the nearest whole degree, in quadrant I, the angle would be 44° too.

In quadrant 2, the angle would be 180° -44°= 136°.