Answer:
The measure of side AB is 6√3 cm.
Step-by-step 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:
[tex]tan\ \theta^{\text{o}}=\frac{Perpendicular}{Base}[/tex]
In the triangle ABC, the perpendicular side is side BC and the base is AB.
Compute the length of side AB as follows:
[tex]tan\ 30^{\text{o}}=\frac{BC}{AB}[/tex]
The value of tan 30° is,
[tex]tan\ 30^{\text{o}}=\frac{1}{\sqrt{3}}[/tex]
The value of side AB is:
[tex]tan\ 30^{\text{o}}=\frac{BC}{AB}[/tex]
[tex]\frac{1}{\sqrt{3}}=\frac{6}{AB}\\\\AB=6\times \sqrt{3}\\AB=6\sqrt{3}[/tex]
Thus, the measure of side AB is 6√3 cm.
