Question

In the adjacent figure, AC = 6 cm, AB = 5 cm and ∠BAC = 30º. Find the area of the triangle.

Answer 1

Since the height is not given we can solve using another formula.

Area of Triangle = Base * Side * Sin Ф / 2

Here let us take the base to be 6 cm and the side measure to be 5 cm.

Substituting in the formula we get,

Area of triangle = 6 * 5 * Sin 30 / 2

=> Area = 30 * ( 1 / 2 ) / 2

=> Area = 30 * 1 / 4

=> Area = 30 * 0.25 = 7.5

Hence the area of the Triangle given is 7.5 cm²

Hope it helped !

Answer 2

In Triangle ABC ,

AC = 6 cm ,

AB = 5 cm

<BAC = 30°

Draw BD perpendicular to AC

In ∆ ADB ,

Sin 30° = BD/AB

=> 1/2 = BD/5

=> BD = 5/2 cm

Now ,

Area of the ∆ABC = ( 1/2 )×base×height

= (1/2) × AC × BD

= ( 1/2 ) × 6cm × ( 5/2 ) cm

= ( 15/2 ) cm²

= 7.5 cm²

I hope this helps you.

: )