In the following triangle, what is the length of the hypotenuse?

Step-by-step explanation:

using trigonometric ratios,

sin theta= opposite ÷ hypoteneus (h)

sin 45°= 3 root 2 ÷ h

1/root 2= 3 root 2 ÷h

h= 3× root 2 × root 2

= 3×2

= 6 unit

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

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