Question

In triangle ABC AB=6√3 AC=12cm and BC=6cm. The angle B is -
a.120
b.60
c.90
d.45
Please give the right answer only in one word.

Answer 1

Answer:

c. 90°

Step-by-step explanation:

According to Pythagoras Theorem,

AC² =AB² +BC²

12²=(6√3)² +6²

144=144

Since this condition satisfies the Pythagoras Theorem, ∠B=90°

Answer 2

Given :

In ∆ABC given sides are ;

$\dashrightarrow \sf{} \: AB = 6\sqrt{3}cm \\ \\ \sf{} \dashrightarrow \: BC = 6cm \\ \\\dashrightarrow \sf{}AC = 12cm$

To Find :

Which type of Triangle has the given sides ?

Solution:

Concept to be used :

In a right angled triangle, the square of the Hypotenuse is equals to the sum of the squares of the other side.

Using this theorem, we would check whether given triangle is Right angled or not.

Therefore,

Since, the largest side is AC it would be Hypotenuse.

Now,

Calculation :

$\sf{}(Hypotenuse {)}^{2} =( Base {)}^{2} +( Perpendicular {)}^{2} \\ \\ \sf{}AC {}^{2} = AB { }^{2} + BC {}^{2} \\ \\ \sf{}(12 {)}^{2} = (6 \sqrt{3} {)^{2} } + (6 {)}^{2} \\ \\ \sf{}144 = 6(3) + 36 \\ \\ \sf{}144 = 108 + 36 \\ \\ \sf{}144 = 144$

Hence, Since LHS = RHS Therefore it verifies our condition to be right angled triangle.

Final Answer:

Therefore, Option (c) 90° is correct and final answer.