Question

Find the area of the right triangle △DEF with the points D (0, 0), E (1, 1), and F.

m∠DEF = 60°.

Answer 1

The area of the triangle is
`√(3)`

Explanation:

Given:

Coordinates D (0, 0), E (1, 1)

Angle ∠DEF = 60°

△DEF is a Right triangle

To Find:

The area of the triangle

Solution:

The area of the triangle is =
`(1)/(2)(base * height)`

Here the base is Distance between D and E

calculation the distance using the distance formula, we get

DE =
`√((0-1)^2 + (0-1)^2)`

DE =
`\sqrt{(-1) ^2 + (-1)^2`

DE =
`√(1+1)`

DE =
`√(2)`

Base =
`√(2)`

Height is DF

DF =
`tan(60^(\circ)) * DE`

DF =
`√(3) * DE`

DF =
`√(3) *√(2)`

Now, the area of the triangle is

=
`(1)/(2)({√(2))(√(3) * √(2))`

=
`(1)/(2)({√(2))(√(3) √(2))`

=
`(1)/(2)(2√(3) )`

=
`√(3)`