# The hypotenuse of the isosceles rectangle of the triangle is 7. Find the leg.

May 26, 2021 | education

| In an isosceles right-angled triangle, the legs between each other are equal to AB = AC, and the angles at hypotenuse BC are equal to 45.

The first way.

The sine of the angle in a right-angled triangle is equal to the ratio of the opposite leg to the hypotenuse of the triangle.

SinACB = AB / AC.

Sin450 = AB / 7.

√2 / 2 = AB / 7.

AB = 7 * (√2 / 2) = 3.5 * √2 cm.

AC = AB = 3.5 * √2 cm.

Second way.

Let the lengths AB and AC = X cm, then by the Pythagorean theorem:

X ^ 2 + X ^ 2 = BC ^ 2.

2 * X ^ 2 = 7 ^ 2.

X ^ 2 = 49/2.

X = 7 / √2 = 7 * √2 / √2 * √2 = 7 * √2 / 2 = 3.5 * √2 cm.

AC = AB = 3.5 * √2 cm.

Answer: The legs of the triangle are 3.5 * √2 cm.

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