Question

This problem refers to triangle ABC. If A = 80°, B = 60°, and b = 15 cm, find a. (Round your answer to the nearest whole number.)

a = ? cm

Answer 1

Explanation:

We can use the law of sines to find the length of side a. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. In other words:

a/sin A = b/sin B = c/sin C

where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the angles opposite those sides.

We are given that A = 80°, B = 60°, and b = 15 cm. We can substitute these values into the law of sines and solve for a as follows:

a/sin 80° = 15/sin 60°

Multiplying both sides by sin 80°, we get:

a = 15*sin 80°/sin 60°

Using a calculator, we can evaluate sin 80° and sin 60° as follows:

sin 80° ≈ 0.9848

sin 60° = √3/2 ≈ 0.8660

Substituting these values, we get:

a ≈ 15*0.9848/0.8660

a ≈ 17.06

Rounding this to the nearest whole number, we get:

a ≈ 17

Therefore, the length of side a is approximately 17 cm.

Answer 2

To solve for side a, we can use the law of sines:

a/sin(A) = b/sin(B)

Substituting the given values:

a/sin(80°) = 15/sin(60°)

a = (15 sin(80°))/sin(60°)

a ≈ 17 cm (rounded to the nearest whole number)

Therefore, side a is approximately 17 cm.