Question

A right triangle has a leg that is 2.70 m long and a hypotenuse that is 7.76 m long. What is the length of the other leg of the triangle in meters using the rules for significant digits?

Answer 1

Applying the Pythagorean Theorem and using the rules of significant digits, the length of the other leg of the right triangle is approximately 2.61 meters.

Recall:

• Pythagorean Theorem is given as: $a^2 + b^2 = c^2$
• a and b are the two other legs of a right-angled triangle, while c is the hypotenuse.

Using the Pythagorean Theorem, we are going to find the length of the other leg of the triangle that has:

• a = 2.70 m (a leg)
• c = 7.76 m (hypotenuse)

• Substitute and find the value of b (the other leg).

$2.27^2 + b^2 = 7.76^2\\\\b = \sqrt{7.76^2 - 2.27^2} \\\\b = 2.607$

Therefore, applying the Pythagorean Theorem and using the rules of significant digits, the length of the other leg of the right triangle is approximately 2.61 meters.

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