Question

Each of two equal sides of an isosceles triangle are 20cm in length and the included angle is 45 degrees. How do we find the third side and the area of the triangle?

Answer 1

The third side `=28.28` cm,
The area `=200` cm squared

Explanation:

There are two ways you can use:

First way: using our knowledge of the two special triangles, we know that the ratio of the legs of a 45-45-90 triangle is `1:1:sqrt2`

so `20sqrt2=28.28` cm

The second method: using trigonometry we know that `sin45=frac(opp)(hyp)`

`0.7071=frac(20)(hyp)`

`hyp=28.28` cm

The area of a triangle is `A=1/2bh`
since the base and height are both `=20`
`A=1/2*20*20`
The area `=200` cm squared