Question

Firefighters dig a triangular trench around a forest to prevent the fire from spreading. Two of the trenches are 800 m long and 650 m long. the angle between them is 30°. Determine the area that is enclosed by these trenches.

Answer 1

130000m^2

Explanation:

a = 800m

b = 800m

c= 650m

α = 30°

4th he triangular trench is an isosceles triangle.

Area of a triangle = 1/2(bcsinA)

= 1/2(800*650*sin30°)

= 130,000m^2

Answer 2

The area enclosed by the trenches is 130 000
`m^(2)`

Explanation:

The two given sides of the trenches are 800m and 650m. Since the included angle of the two sides are given, then the area covered by the trenches can be calculated using the formula;

Area of a triangle =
`(1)/(2)` × abSin C

where: a is the length of one side and b the length of the second side and C represents the value of the included angle.

Thus,

a = 800m, b = 650m and C = 30°

So that,

Area enclosed by the trenches =
`(1)/(2)` × abSin C

=
`(1)/(2)` × 800 × 650 × Sin30°

=
`(1)/(2)` × 800 × 650 × 0.5

= 130 000

The area enclosed by the trenches is 130 000
`m^(2)`.