In the right triangle shown, ∠a=30° and ab = 12√3 how long is ac

Solution :

Given that in the right triangle , ∠A=30° and AB = 12√3 .

As the figure is missing and its not clearly mentioned that AB is the base or hypotenuse of the right triangle. So two cases arises-

Case 1: AB is the base for ∠A of  the right triangle (as shown in figure 1).

As we know from the trigonometric ratio that,

Here , AB is the base and AC is the hypotenuse , and ∠A=30°

The value of

Hence, AC is 24 unit long.

Case 2: AB is the hypotenuse for ∠A of  the right triangle (as shown in figure 2).

As we know from the trigonometric ratio that,

Here , AB is the hypotenuse and AC is the base, and ∠A=30°

The value of

Hence, AC is 18 unit long.

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