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The side length of an equilateral triangle is 5 centimeters. Find the length of an altitude. Round your answer to the nearest tenth.
The length of the altitude is about
◻ centimeters.

The side length of an equilateral triangle is $5$ centimeters. Find the length of an altitude. Round your answer to the nearest tenth. $\newline$ The length of the altitude is about $\square$ centimeters.

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Pythagorean theorem

Full solution

Q. The side length of an equilateral triangle is

5

centimeters. Find the length of an altitude. Round your answer to the nearest tenth.

\newline

The length of the altitude is about

\square

centimeters.

Draw Triangle and Altitude: question_prompt: What's the length of the altitude in an equilateral triangle with side length $5\,\text{cm}$ ?
Identify Right Triangles: Draw the triangle and altitude, the altitude creates two $30$ - $60$ - $90$ right triangles.
Use $30$ $-60$ $-90$ Triangle Property: In a $30$ $-60$ $-90$ triangle, the length of the altitude $a$ is $\sqrt{3}/2$ times the length of the hypotenuse $h$ .
Calculate Altitude Length: Calculate the altitude using the formula $a = h \times (\sqrt{3}/2)$ , where $h = 5$ cm.
Perform Calculation: $a = 5 \times (\sqrt{3}/2) = 5 \times 1.732/2 = 5 \times 0.866 = 4.33$ cm.
Round to Nearest Tenth: Round the answer to the nearest tenth: $4.33\,\text{cm}$ rounds to $4.3\,\text{cm}$ .

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