Solve ∆ABC given angle A = 58ᵒ, b = 10.0 cm, and c = 14.0 cm. Round to one decimal place.

Answer 1

To solve ∆ABC, we need to use the Law of Sines which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

First, we need to find angle B using the Law of Sines:

sin(B)/10.0 = sin(58°)/14.0

Cross-multiplying, we get:

sin(B) = (10.0 * sin(58°))/14.0

sin(B) ≈ 0.5842

Taking the inverse sine, we find that angle B is approximately 35.3°.

To find angle C, we know that the sum of all angles in a triangle is always 180°:

180° = 58° + 35.3° + angle C

angle C ≈ 86.7°

Now that we have all three angles, we can find the length of side a using the Law of Sines once again:

sin(58°)/10.0 = sin(86.7°)/a

Cross-multiplying, we get:

a = (10.0 * sin(86.7°))/sin(58°)

a ≈ 11.5 cm

Therefore, the lengths of the sides of ∆ABC are approximately:

a ≈ 11.5 cm
b = 10.0 cm
c = 14.0 cm