# Find the AC side of a right-angled triangle ABC if BC = 9 cm and AB = 7 cm.

August 25, 2021 | education

| It is known from the condition that the right-angled triangle that we are given ABC has side lengths BC = 9 cm, and AB = 7 cm.

To find the third side of triangle AC. since we do not know where the right angle of the triangle is, we will consider AC as the hypotenuse and as the leg of the triangle.

So AC is the hypotenuse of the triangle. Let’s apply the Pythagorean theorem:

c ^ 2 = a ^ 2 + b ^ 2;

AC = √ (BC ^ 2 + AB ^ 2) = √ (9 ^ 2 + 7 ^ 2) = √ (81 + 49) = √130 cm.

AC is the leg of the triangle.

a ^ 2 = c ^ 2 – b ^ 2;

AC = √ (BC ^ 2 – AB ^ 2) = √ (81 – 49) = √32 = 4√2 cm.

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