Two sides of a triangle and their included angles are 4cm, 5cm and 30 degree resp. What is the area.

Please check attached image for detailed figure and explanation (ignore my handwriting

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Option 1: If we see 5 and 4 as sides, we usually go with right triangle and find 3rd side with Pythagoras theorem.

so 3rd side here = 3 . And area becomes 1/2 *4*3 =6

But its

wrong answer as for right triangle 3,4,5 the angle between sides 5 and 4 is not 30 degree.

(Here non of the option is 6 so most likely we will not make this mistake)

Option 2: (Check attached img for diagram)

If we consider 5cm as base, we can draw a triangle using 4cm as 1 side and angle 30degree between them .

To find height of triamgle, drop perpendicular from 4cm side on 5cm base. Height can be calculated as we know angle = 30 degree.

So height = sin30 * 4cm = 2

so Area = 1/2 *5*2 = 5

Answer: COption 3: Using formula

Area formula if we know 2 sides of triangle and the angle between them =>

\(Area = \frac{a*b* Sin C}{2}\)

\(Area =\frac{4*5*Sin30}{2}\)

Area = 4*5*(1/2) /2 = 5

Answer: C
Attachments

Triangel with sides and angle.jpg [ 1.63 MiB | Viewed 637 times ]