Question

ABC is a right triangle. ∠C is a right angle,  m A ∠ =50 , and AB = 40 cm.

a. Sketch and label the triangle.
b. Determine the lengths of AC and BC .

Answer 1

Explanation:

The sketch of the triangle is shown in the attached photo.

From the given right angle triangle,

AB represents the hypotenuse of the right angle triangle.

With m∠A as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine AC, we would apply

the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos 50 = AC/40

AC = 40Cos50 = 40 × 0.643

AC = 25.72 cm

To determine BC, we would apply

the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 50 = BC/40

BC = 40SinS0 = 40 × 0.766

BC = 30.64 cm