Answer:
Step-by-step explanation:
The given triangle is a right angle triangle and also an isosceles triangle.
The hypotenuse is the longest side of the right angle triangle. To determine the hypotenuse, we will apply trigonometric ratio
Sin θ = opposite side/hypotenuse
Looking at the triangle.
θ = 45 degrees = 1/√2
opposite side = 3√2
Therefore,
Sin 45 = 3√2/hypotenuse
1/√2 = 3√2/hypotenuse
hypotenuse × 1 = √2 × 3√2
hypotenuse = 3√2 × √2
hypotenuse = 3 × 2 = 6
Alternatively,
We can apply Pythagoras theorem since both sides are equal
Since the length of one side is 3√2, then the length of the other side is also 3√2
Hypotenuse^2 = opposite side^2 + adjacent side^2
Hypotenuse^2 = (3√2)^2 + (3√2)^2
Hypotenuse^2 = 18 + 18 = 36
Hypotenuse = √36 = 6
