Question

Consider the triangle shown in the diagram below.Suppose that m∠A=80∘, a=6.17, and b=4.22. (The diagram above is not necessarily to scale.)What is the value of m∠B?m∠B=  °   What is the value of c?c=

Answer 1

Using the law of sines, we found that m∠B ≈ 43.7° and c ≈ 3.98 for the given triangle with m∠A=80∘, a=6.17, and b=4.22.

a. To find the value of m∠B, we can use the law of sines, which states that a/sinA = b/sinB.

Rearranging this equation to solve for sinB, we get sinB = (b/a) * sinA.

Plugging in the given values, we get sinB = (4.22/6.17) * sin(80°) ≈ 0.686.

Taking the inverse sine of this value, we find that m∠B ≈ 43.7°.

b. To find the value of c, we can again use the law of sines.

Using the same equation as before, but solving for c instead, we get c = (a * sinB)/sinA.

Plugging in the known values, we get c = (6.17 * sin(43.7°))/sin(80°) ≈ 3.98.

Answer 2

[tex]\begin{gathered} a)Step-by-step explanation

a) To find the measure of apply sine rule that states that:

Therefore:

[tex]\frac{\sin(Therefore, for the given triangle:[tex]\begin{gathered} \frac{\sin80}{6.17}=\frac{\sin (That is the measure of

b) To find c, we first have to find The sum of angles in a triangle is 180°.

Therefore:

[tex]\begin{gathered} Now, apply sine rule:[tex]\begin{gathered} \frac{\sin(That is the value of c.