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

Answer:

The hypothenuse is 10 meters long.

Step-by-step 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 $5\sqrt{2}$.

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

$sin \theta =\frac{opposite}{hypothenuse}\\ sin 45\°=\frac{5\sqrt{2} }{h}$

Now, we solve for $h$

$h=\frac{5\sqrt{2} }{sin45\°}\\ h=\frac{5\sqrt{2} }{\frac{\sqrt{2} }{2} } \\h=\frac{10\sqrt{2} }{\sqrt{2} }\\ h=10$

Thereofre, the hypothenuse is 10 meters long.