Question

Find the value of a and the area of the triangle. Round to the nearest hundredth

Answer 1

a = 6.65

Area = 15.84

Explanation:

By cosine rule in the given triangle,

BC² = AC² + AB² - 2(AC)(AB)cos(C)

a² = 5² + 9²- 2(5)(7)cos(28°)

a² = 25 + 81 - 61.81

a =
`√(44.19)`

a = 6.65

Area of a triangle with given three sides =
`√(s(s-a)(s-b)(s-c))`

Here, s = Average of lengths of all sides

a, b and c are the measures of the respective sides of the triangle.

s =
`(6.65+7+5)/(2)`

s = 9.325

a = 6.65, b = 5 and c = 7

Now substitute these values in the formula to get the area,

Area =
`√(9.325(9.325-6.65)(9.325-5)(9.325-7))`

=
`√(9.325* 2.675* 4.325* 2.325)`

=
`√(250.8313)`

= 15.838

= 15.84