Question

Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown.

What is the greatest possible whole-number length of the unknown side?

8 inches
9 inches
12 inches
13 inches

Answer 1

Answer. 9 inches

1. Using some logical reasoning(Not proving because it will take a while) as the acute angle approaches to 90° the side in front of that angle extends.

2. Lets find the third side if the angle is 90° -> Using Pythagoras's theorem` hypotenuse(the side)=√(5*5+8*8) which is approximately 9.433 inches.

3. As we need to find the largest possible length of the unknown side its 9 inches, which is the biggest integer below 9.4.

Answer 2

The greatest possible whole-number length of the unknown side is 9 inches

What is an acute triangle?

An acute triangle is a triangle with three different sides and the angles of each side in the triangle is less than 90°.

Using the Pythagoras' rule to determine the length of the unknown side, we have:

• hypotenuse² = opposite² + adjacent²

• the hypotenuse is usually the longest side
• the line facing the hypotenuse is the opposite
• the adjacent has the smallest size and it is usually the base.

hypotenuse² = (8 in)² + (5 in)²

hypotenuse² =  64 in + 25 in

hypotenuse² = 89 in

hypotenuse = $\mathbf{\sqrt{89 \ inches}}$

hypotenuse = 9.43 inches

hypotenuse ≅ 9 inches

Learn more about acute triangles here:

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