Question

In a right triangle, if ∠θ=45° and the side opposite to this angle is 5√2 meters, what is the approximate length of the hypotenuse?

Answer 1

sine 45 degrees = opp / hyp
hypotenuse = 5*sqrt(2) / sine(45)
hypotenuse = 5*sqrt(2) /.70711
hypotenuse = 9.9999544793
hypotenuse is 10.

Answer 2

The hypothenuse is 10 meters long.

Explanation:

We know by defintion that a right triangle has a righ angle which is equal to 90°.

So, by given, we know that one of the acute angles is 45°, that means the other acute angle is also 45°, because all three internal angles must sum 180°.

Now, the given angle is

`\theta =45\°`

And its opposite side is
`5√(2)`.

To find the hypothenuse we need to use the sin function, which relates the angle with its opposite side and the hypothenuse.

`sin \theta =(opposite)/(hypothenuse)\\ sin 45\°=(5√(2) )/(h)`

Now, we solve for
`h`

`h=(5√(2) )/(sin45\°)\\ h=(5√(2) )/((√(2) )/(2) ) \\h=(10√(2) )/(√(2) )\\ h=10`

Thereofre, the hypothenuse is 10 meters long.