Question

Sketch a 45-45-90 triangle and indicate the angle measures and side lengths if one leg measures 1 inch.

Answer 1

If we want to sketch a triangle with angle of 45-45-90 we know that it's a right triangle, because of the 90º angle

the we can use the trig relationships:

`\sin (45º)=(1)/(h)`

And:

`\cos (45º)=(1)/(h)`

By pytagoras:

`h^2=l^2+L^2`

Where l and L are the two legs, since the angles are equal, l and L are equal:

`\begin{gathered} \cos (45)=(1)/(h) \\ \sin (45)=(1)/(h) \end{gathered}`

Then:

`\begin{gathered} (1)/(h)=\sin (45) \\ h=\sqrt[]{2} \end{gathered}`

By pythagoras:

`\begin{gathered} (\sqrt[]{2})^2=((1)/(\sin(45)))^2+((1)/(\cos 45))^2 \\ 2=1+1 \end{gathered}`

Then we know that the length og each side is √1 which is 1, and then added to the other leg, 1 + 1 = 2

By the angles 45º, 45º and 90º and one leg of length 1, the sides are 1, 1 and 2