UPSC NDA Math Model Paper 1

Concept:
Let AB,BC, And AC are the sides of triangle ABC then, Area of triangle =‌

1

2

|AB|.|AC|.sin‌A
Calculations:
Given, Let ∆ABC be a triangle whose area is 10√3 units with side lengths |AB|=8 units and |AC|=5 units.
Area of triangle =‌

1

2

|AB|.|AC|.sin‌A
⇒10√3=‌

1

2

8.5.sin‌A
⇒10√3=20‌sin‌A
⇒sin‌A=‌

√3

2

⇒A=60∘ or 120∘
Hence, Let ∆ABC be a triangle whose area is 10√3 units with side lengths |AB|=8 units and |AC|=5 units. then the possible values of the angle A are 60∘ or 120∘.