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
[tex]\theta =45\°[/tex]
And its opposite side is [tex]5\sqrt{2}[/tex].
To find the hypothenuse we need to use the sin function, which relates the angle with its opposite side and the hypothenuse.
[tex]sin \theta =\frac{opposite}{hypothenuse}\\ sin 45\°=\frac{5\sqrt{2} }{h}[/tex]
Now, we solve for [tex]h[/tex]
[tex]h=\frac{5\sqrt{2} }{sin45\°}\\ h=\frac{5\sqrt{2} }{\frac{\sqrt{2} }{2} } \\h=\frac{10\sqrt{2} }{\sqrt{2} }\\ h=10[/tex]
Thereofre, the hypothenuse is 10 meters long.
