Question

En el triángulo rectángulo que se muestra, \angle A = 30^\circ∠A=30 ∘ angle, A, equals, 30, degrees y BC = 6BC=6B, C, equals, 6. ¿Cuánto mide ABABA, B?

Answer 1

The measure of side AB is 6√3 cm.

Explanation:

The question is:

In the right triangle shown, ∠A = 30° and BC = 6. What is AB?

Solution:

Consider the right-angled triangle ABC below.

In the triangle:

∠A = 30°

∠B = 90°

BC = 6 cm

According to the trigonometric identities for a right-angled triangle the tangent of an angle is the ratio of the length of perpendicular side to the length of the base.

That is for angle θ° the value of tan θ° is:

`tan\ \theta^{\text{o}}=(Perpendicular)/(Base)`

In the triangle ABC, the perpendicular side is side BC and the base is AB.

Compute the length of side AB as follows:

`tan\ 30^{\text{o}}=(BC)/(AB)`

The value of tan 30° is,

`tan\ 30^{\text{o}}=(1)/(√(3))`

The value of side AB is:

`tan\ 30^{\text{o}}=(BC)/(AB)`

`(1)/(√(3))=(6)/(AB)\\\\AB=6* √(3)\\AB=6√(3)`

Thus, the measure of side AB is 6√3 cm.