Question

If sides A and B of a triangle have lengths of 5 and 9 respectively, and the angle between them is `(pi)/4`, then what is the area of the triangle?

Answer 1

`( 45sqrt2)/4 ≈ 15.91" square units "`

Explanation:

Given a triangle , where 2 sides and the angle between them are known, then the area of the triangle can be calculated using

Area = `1/2 ABsintheta`

where A and B are the 2 sides and `theta`, the angle between them

here A = 5 , B = 8 and `theta = pi/4`

hence area `= 1/2xx5xx9xxsin(pi/4) = 45/(2sqrt2)`

where the exact value of `sin(pi/4) = 1/sqrt2`

Rationalising the denominator of the fraction, to obtain

area `= 45/(2sqrt2) = (45sqrt2)/4 ≈ 15.91" square units "`