Question

the angles A,B and C of a triangle ABC are in AP if AB=6 , BC=7 then find AC

Answer 1

i hope this will help you

Answer 2

Answer:

6.557

Step-by-step explanation:

We are given that the angles A,B and C of a triangle ABC are in AP

Let the angles be a-d ,a , a+d

a-d+a+a+d = 180 (Angle sum property of triangle )

3a= 180

a = 60

Now to find AC we will use cosine law

Formula: $c^2=a^2+b^2-2abcosc$

$AC^2=AB^2+BC^2-2(AB)(BC)cos B$

$AC^2=6^2+7^2-2(6)(7)cos 60$

$AC^2=6^2+7^2-2(6)(7) \frac{1}{2}$

$AC^2=6^2+7^2-(6)(7)$

$AC=\sqrt{6^2+7^2-(6)(7)}$

$AC=6.557$

Hence AC is 6.557