Question

What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer. Triangle A B C is shown. Angle C A B is 66 degrees and angle A B C is 76 degrees. The length of A B is 3 and the length of A C is b. Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction 1.9 units 4.7 units 5.0 units 5.7 units

Answer 1

4.7 units

Explanation:

Answer 2

4.7 units

Explanation:

We are given that in triangle ABC

AB= 3 units

Angle ABC=76 degree

Angle CAB=66 degrees

AC=b

We have to find the approximate value of b using sin laws.

We know that sum of angles of a triangle =180 degrees

`\angle CAB+\angle ABC+\angle ACB=180`

`76+66+\angle ACB=180`

`142+\angle ACB=180`

`\angle ACB=180-142=38^(\circ)`

We know that law of sines

`(BC)/(Sin A)=(AC)/(SinB)=(AB)/(sin C)`

Substitute the values then we get

`(b)/(sin 76^(\circ))=(3)/(sin 38^(\circ))`

`b=(3)/(sin 38^(\circ))* sin 76^(\circ)`

`b=4.7`

Hence, the value of b= 4.7 units