Question

From the diagram below, if the measure of < C = 30 °, and side BC = 15, then side AB = _____.

Answer 1

The value of the unknown side AB is 5√3 (option D)

To solve the unknown side of the right angle triangle, we will use trigonometry function.

Given:

<C (θ) = 30°

BC = 15

AB = ?

We use Tan θ = AB / BC

Tan 30° = AB / 15

AB = Tan 30° x 15

To calculate (Tan30°) x 15:

1. Find the tangent of (30°):

tan(30°) = sin(30°) / cos(30°)

Use the values;

(sin30°) = 1/2

(cos30°) = √3/2

Therefore;

tan(30°) = (1/2) / (√3/2)

tan(30°) = (1/√3)

2. Multiply both sides by 15:

AB = tan(30°) x 15

AB = (1/√3) x 15

To rationalize the denominator, multiply both the numerator and denominator by (√3):

AB = (1/√3) x 15 x (√3/√3)

AB = (15√3) ÷ 3

AB = 5√3

Therefore, option D (5√3) is the correct answer. The value of the unknown side AB is 5√3

Answer 2

To solve this problem, we will use the trigonometric function tangent.

Recall that by definition, in a right triangle:

`tan\theta=\frac{opposite\text{ leg}}{adjacent\text{ leg}}.`

Therefore:

`tan30^(\circ)=(AB)/(15).`

Solving for AB, we get:

`AB=tan30^(\circ)*15.`

Finally, we get:

`AB=5√(3).`

Answer:

`5√(3).`