Question

In ∆ABC, if c2 + a2 - b2 = ac, then ∠ B = __________.

Answer 1

Step-by-step explanation:

All sides of a ∆ = 180°

a^2 + b^2 + c^2=180°

=180/3 = 60°

sin60° = π/3

cos60° = π/3

ans:- π/3

Answer 2

Final Answer:

In the triangle $\triangle ABC$, where $c^2 + a^2 - b^2 = ac$ the value of the angle $\angle B$ is sixty degrees ($60\textdegree$).

Given:

In the triangle $\triangle ABC$, the provided condition is $c^2 + a^2 - b^2 = ac$

To Find:

The value of the angle $\angle B$ in the triangle $\triangle ABC$, where $c^2 + a^2 - b^2 = ac$ is to be calculated.

Explanation:

The concepts that are important to find the solution are as follows

• In any triangle $\triangle ABC$, the sides opposite to the angles $\angle A,\;\angle B, \;\angle C$ are a, b, and c respectively.
• The value of cos B in the triangle $\triangle ABC$ is  $cos B=\frac{c^2 + a^2 - b^2 }{2ac}$.
• The trigonometric value $cos60\textdegree=\frac{1}{2}$

Step 1 of 2

Using the information in the given problem, write the following.

$cos B\\\\=\frac{c^2 + a^2 - b^2 }{2ac}\\\\=\frac{ac }{2ac}\;\;\;\;\;\;[c^2 + a^2 - b^2 = ac]\\\\=\frac{1}{2}$

Step 2 of 2

In continuation with the above calculations, write and solve the following equation.

$cos B=\frac{1}{2} \\cosB=cos60\textdegree\\B=60\textdegree$

Therefore, the required correct answer is $\angle B=60\textdegree$.

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https://brainly.in/question/38417

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