I have an attached a picture of a right triangle below so you can understand it more. :)
We know that the height of line AB is 15 meters, and the adjacent angle is 45°. The adjacent angle is the angle beside the side.
Since we want to know the length of the hypotenuse this would involve trigonometry. Whenever trigonometry is involved we need to let the triangle be a right triangle.
Since ∠CAB=45° and ∠ABC=90° therefore ∠ACB=180°-90°-45°=45°
(We got 180° since it is the sum of the interior angles of a triangle.)
Since ∠CAB=∠ACB=45° This would mean that the triangle is a right isosceles triangle and AB=BC=15 meters.
The Pythagorean Theorem states that:
[tex]a^2+b^2=c^2[/tex]
This is where a and b are the side lengths of the legs and c is the length of the hypotenuse. This theorem only works in right triangles. This can be further simplified to:
[tex] \sqrt{a^2+b^2} =c[/tex]
Our a and b are equal since AB=BC=15 meters so we substitute it to the simplified version and we get:
[tex]AC= \sqrt{15^2+15^2} \\ =\sqrt{2(15^2)} \\ =15 \sqrt{2} [/tex]
You can also notice that the triangle is a 45-45-90 triangle which means that the legs are both equal to x and the hypotenuse is equal to [tex]x \sqrt{2} [/tex].We know that x is 15 so the hypotenuse would be [tex]15* \sqrt{2} [/tex]
Therefore the length of the hypotenuse is [tex]15 \sqrt{2} [/tex] meters.
