Question

In δABC, BC = 620 cm, ∠C=106° and ∠A=48°. find the length of AC, to the nearest centimeter.

A) 310 cm
B) 408 cm
C) 540 cm
D) 572 cm

Answer 1

To find the length of AC in triangle ABC, we can use the Law of Sines to set up an equation and solve for x. Substituting the given values, we find that the length of AC is approximately 408 cm.

Step-by-step explanation:

To find the length of AC in triangle ABC, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. Let's denote the length of AC as x. Using the Law of Sines, we have:

sin(A)/x = sin(B)/BC

Substituting the given values, we have:

sin(48°)/x = sin(106°)/620

Cross-multiplying and rearranging the equation, we get:

x = (sin(48°) * BC) / sin(106°)

Calculating this, we find that x ≈ 408 cm.