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

Answer:

4.7 units

Step-by-step explanation:

Answer 2

Answer:

4.7 units

Step-by-step 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

$\frac{BC}{Sin A}=\frac{AC}{SinB}=\frac{AB}{sin C}$

Substitute the values then we get

$\frac{b}{sin 76^{\circ}}=\frac{3}{sin 38^{\circ}}$

$b=\frac{3}{sin 38^{\circ}}\times sin 76^{\circ}$

$b=4.7$

Hence, the value of b= 4.7 units