The hypotenuse of an isosceles right-angled triangle is 7 √2. Find the leg.
| January 17, 2021 | education
First way.
Since the triangle is isosceles and right-angled, its legs are equal, and the angles at the hypotenuse are equal to 450.
The sine of the angle of a right-angled triangle is the ratio of the opposite leg to the hypotenuse.
SinACB = AB / BC.
Sin45 = AB / (7 * √2).
AB = (√2 / 2) * (7 * √2) = 7 cm.
AC = 7 cm.
Second way.
Let AB = BC = X.
By the Pythagorean theorem, X ^ 2 + X ^ 2 = (7 * √2) ^ 2.
2 * X ^ 2 = 49 * 2.
X = √49 = 7 cm.
AB = BC = 7 cm.
Answer: The legs of the triangle are 7 cm.
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