In the triangle ABC, AB = 12 cm, angle BAC = 60◦ and angle ACB = 45◦. Find the exact length \ \ of BC.

Step 1:

$\"\"$ length of the $\"\"$ is $\"\"$ .

Angles are $\"\"$ is $\"\"$ and $\"\"$ is $\"\"$ .

Find $\"\"$ length.

The law of sines : $\"\"$

Draw the $\"\"$ .

$\"\"$

Observe the $\"\"$ :

Substitute $\"\"$ and $\"\"$ in the law of sines. \ \

$\"\"$

Equate first and last terms.

$\"\"$

Substitute $\"\"$ and simplify. \ \

$\"\"$

Therefore, $\"\"$ length of the $\"\"$ is $\"\"$

Solution :

The length of the $\"\"$ is $\"\"$ .