Question

Use a special right triangle to express the cosine of 45 degree as a fraction and as a decimal to the nearest hundredth

Answer 1

The special triangle you need is a right isosceles triangle, with legs 1 and hypotenuse
`√(2)`.

As for every right triangle, you can find of the cosine of an angle using the "adjacent/hypotenuse" ratio.

In this case, the two base angles are equal, and so are the two legs. So, it doesn't matter which angle or leg you'll choose, the ratio will be

`\cos(45)=(1)/(√(2))`

which indeed is both the sine and cosine of 45°

Its approximated value is 0.707...