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

The answer is 5h= nStep-by-step...

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

johndoesnutz4690

11.03.2022

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, $cos(\theta) = \frac{base}{hypotenuse}$

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

$\Rightarrow cos(30)=\frac{AB}{AC} \\\\\Rightarrow AC=\frac{AB}{cos(30)}$

The value of $cos(30)=\frac{\sqrt{3} }{2}$

$\Rightarrow AC=12\sqrt{3}\times\frac{2 }{\sqrt{3} }\\\\\Rightarrow AC=24$

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, $cos(\theta) = \frac{base}{hypotenuse}$

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

$\Rightarrow cos(30)=\frac{AC}{AB} \\\\\Rightarrow AC=AB\timescos(30)$

The value of $cos(30)=\frac{\sqrt{3} }{2}$

$\Rightarrow AC=12\sqrt{3}\times\frac{\sqrt{3}}{2}\\\\\Rightarrow AC=18$

Hence, AC is 18 unit long.

0,0(0 оценок)