In 0394abc, If The Length Of Side B Is 3 Centimeters And The Measures Of 2220b And 2220c Are 45\Xb0 And 60\Xb0, Respectively, What Is The Length Of Si

In ΔABC, if the length of side b is 3 centimeters and the measures of ∠B and ∠C are 45° and 60°, respectively, what is the length of side c to two decimal places?

 

Answer:

The length of side c is 3.68 cm.

Step-by-step explanation:

For any oblique triangle (non-right triangle) given the measurement of its two angles and a side (Side-Angle-Side/SAS or Angle-Angle-Side/AAS), apply the Law of Sines to find the unknown measurements of a side of angle.

Law of Sines:

a/SinA = b/SinB = c/SineC

Where:

a, b, and c are the sides opposite the interior angles A, B, and C, respectively.

Given:

b = 3 centimeters

B = 45°

c =unknown

C = 60°

Find the length of side c:

b/SinB = c/SinC

3/Sin 45° = c/Sin 60°

(Sin 45°) (c) = (3) (Sin 60°)

c = (3) (Sin 60°) / (Sin 45°)

c = (3) (0.866) /( 0.707)

c = 2.598/0.707

c ≈ 3.67468  or 3.675

c ≈ 3.68 cm  (up to two decimal places)


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