Question

Find the exact area of thetriangle below.

Answer 1

I am going to draw a picture to ilustrate the solution

Now, we are going to use the trigonometric functions for the right triangle on the left to calculate h

`\sin (30)\text{ = }\frac{h}{10\sqrt[]{3}}\Rightarrow\text{ h= sin(30)}\cdot\text{ 10}\sqrt[]{3\text{ }}=(1)/(2)\cdot10\sqrt[]{3}=5\sqrt[]{3}`

Now we use the formula for the area of a triangle

`A=(b\cdot h)/(2)=\text{ }\frac{20\cdot5\sqrt[]{3}}{2}=50\sqrt[]{3}`