Question

In the triangle below, b = _____. If necessary, round your answer to two decimal places.

Answer 1

Answer: The value of b is approximately 54.94 .

Step-by-step explanation:

In the given figure two angles are given and according to the angle sum property the sum of interior angles of a triangle is 180 degree.

`\angle A+\angle B+\angle C=180`

`42+\angle B+41.5=180`

`\angle B=180-83.5`

`\angle B=96.5`

According to the law of sine,

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

From given figure,
`\angle A=42,a=37`

`(37)/(\sin (42^(\circ)))= (b)/(\sin (96.5^(\circ)))`

`(37)/(0,66913) =(b)/(0.99357)`

`b=54.94018`

`b\approx 54.94`

Therefore, the value of b is 54.94.

Answer 2

The Law of Sines is applicable here for quick calculation...

b/sin(180-42-41.5)=37/sin42

b/sin96.5=37/sin42

b=37sin96.5/sin42 units

b≈54.94 units (to nearest hundredth of a unit)