Question

A triangular field has sides 218.5 and 213.3 and the angle between them measures 58.96°. Find the area of the field.

Answer 1

The area of the field = 19966.21 units²

Explanation:

* Lets explain how to find area of a triangle by trigonometry rule

- In any triangle if you have the lengths of two sides and the measure

of the including angle between these two sides, then the area of the

triangle is A =
`(1)/(2)s_(1)s_(2)sin\alpha` , wher α is the

including angle between them

* Lets solve the problem

∵ The field is shaped triangle

∵ The lengths of two sides of the field are 218.5 and 213.3

∴ s1 = 218.5

∴ s2 = 213.3

∵ The measure of the angle between the two sides is 58.96°

∴ α = 58.96°

- Lets find the area using the rule of trigonometry

∴
`A=(1)/(2)(218.5)(213.3)sin(58.96)=19966.21`

∴ The area of the field = 19966.21 units²