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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