Question

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

Answer 1

Answer:

The area of the triangle is  $\sqrt{3}$

Step-by-step 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  = $\frac{1}{2}(base \times height)$

Here the base is Distance between D and E

calculation the distance using the distance formula, we get

DE  = $\sqrt{(0-1)^2 + (0-1)^2}$

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

DE = $\sqrt{1+1}$

DE = $\sqrt{2}$

Base = $\sqrt{2}$

Height is DF

DF =$tan(60^{\circ}) \times DE$

DF = $\sqrt{3} \times DE$

DF = $\sqrt{3} \times\sqrt{2}$

Now, the area of the triangle is

= $\frac{1}{2}({\sqrt{2})(\sqrt{3} \times \sqrt{2})$

=$\frac{1}{2}({\sqrt{2})(\sqrt{3} \sqrt{2})$

=$\frac{1}{2}(2\sqrt{3} )$

=$\sqrt{3}$