Consider triangle ABC. The legs have a length of 5 units each. Triangle A B C is shown. Angle A C B is a right angle. The lengths of sides A C and C B are 5. The length of the hypotenuse c is unknown. What is the length of the hypotenuse of the triangle? 5 units 5 StartRoot 2 EndRoot units 10 units 10 StartRoot 2 EndRoot units

Hypotenuse = 5√2 units

Step-by-step explanation:

Triangle ABC:

The legs are 5 units each

Opposite = 5unit

Adjacent = 5unit

Triangle ACB:

lengths of sides A C and C B are 5

The legs are 5 units each

Leg =AC = Opposite = 5unit

Leg = CB = Adjacent = 5unit

The hypotenuse for both ∆ACB is unknown. Since ∆ACB is a right angled triangle, we would apply Pythagoras theorem to find the hypotenuse.

Using Pythagoras theorem:

Hypotenuse ² = opposite ² + adjacent ²

Hypotenuse ² = leg² + leg²

AB = hypotenuse in ∆ACB

AB² = 5² + 5²

AB² = 25+25 = 50

AB = √50 = √(25×2)

AB = 5√2

Hypotenuse = 5√2 units