Answer:
1) x = 5
2) y = 5·√2
Explanation:
1) The given parameter of the right triangle are;
The legs of the right triangle = 'x', and 5
One interior angle of the right triangle = 45°
Therefore, buy the interior angle summation property of a right triangle, we have;
The measure of the other angle, θ = 180° - 90° - 45° = 45°
From which we have;
A right triangle with an interior angle of 45° is an isosceles triangle with both legs equal
∴ The length of the other leg, x = 5
x = 5
2) By Pythagoras's theorem, we have that the square of the length of the hypotenuse, 'y', is given as follows;
y² = x² + 5²
∴ y² = 5² + 5²
y = √(5² + 5²) = √(25 + 25) = √50 = √(25 ×2) = 5·√2
y = 5·√2 in the simplest radical form.