In triangle ABC, if angle A = 90 degrees and AB = 6 cm, AC = 8 cm, what is the l

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Question: In triangle ABC, if angle A = 90 degrees and AB = 6 cm, AC = 8 cm, what is the length of BC?

Options:

Correct Answer: 10 cm

Solution:

Using the Pythagorean theorem: BC = √(AB² + AC²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

In triangle ABC, if angle A = 90 degrees and AB = 6 cm, AC = 8 cm, what is the length of BC?

In triangle ABC, if angle A = 90 degrees and AB = 6 cm, AC = 8 cm, what is the length of BC?

Step 1: Identify the triangle ABC where angle A is 90 degrees. This means it is a right triangle.
Step 2: Note the lengths of the two sides that form the right angle: AB = 6 cm and AC = 8 cm.
Step 3: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides (AB and AC).
Step 4: Write the formula: BC² = AB² + AC².
Step 5: Substitute the values into the formula: BC² = 6² + 8².
Step 6: Calculate 6², which is 36, and 8², which is 64.
Step 7: Add the two results together: 36 + 64 = 100.
Step 8: To find BC, take the square root of 100: BC = √100.
Step 9: Calculate the square root of 100, which is 10 cm.
Step 10: Conclude that the length of BC is 10 cm.

Pythagorean Theorem – In a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides (AB and AC).