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The height of an equilateral triangle equals 3√2

times the side length. Using 7/4
for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?

5 answers

To calculate the height \( h \) of an equilateral triangle with a side length \( s \), we can use the formula for the height in terms of the side length:

\[ h = \frac{\sqrt{3}}{2} s \]

Given that \( s = 8 \) meters, we substitute this value into the formula:

\[ h = \frac{\sqrt{3}}{2} \times 8 \]

Next, we can substitute \( \sqrt{3} \) with \( \frac{7}{4} \) as per the provided value. First, let's calculate \( \frac{\sqrt{3}}{2} \):

\[ \frac{\sqrt{3}}{2} = \frac{7/4}{2} = \frac{7}{4} \times \frac{1}{2} = \frac{7}{8} \]

Now we can substitute this back into the height formula:

\[ h = \frac{7}{8} \times 8 \]

The \( 8 \)s cancel out:

\[ h = 7 \]

Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is:

\[ \boxed{7} \text{ meters} \]

human answer bub

Sure! Let's break this down step by step in a more straightforward way.

You're looking to find the height of an equilateral triangle with a side length of 8 meters. The height \( h \) of an equilateral triangle can be calculated using the formula:

\[ h = \frac{\sqrt{3}}{2} s \]

where \( s \) is the side length. In your case, \( s = 8 \) meters.

  1. Plug in the side length:

    \[ h = \frac{\sqrt{3}}{2} \times 8 \]

  2. Now using the approximation where \( \sqrt{3} \) is approximately \( \frac{7}{4} \), we replace \( \sqrt{3} \):

    \[ h = \frac{\frac{7}{4}}{2} \times 8 \]

  3. Simplify \( \frac{7}{4} \div 2 \) which is equal to \( \frac{7}{4} \times \frac{1}{2} = \frac{7}{8} \):

    \[ h = \frac{7}{8} \times 8 \]

  4. Finally, calculating this gives:

    \[ h = 7 \text{ meters} \]

So, the height of the equilateral triangle with a side length of 8 meters is approximately 7 meters.

The diagonal of a square equals 2–√
times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side?

To find the diagonal \( d \) of a square in relation to its side length \( s \), we can use the formula:

\[ d = \sqrt{2} \times s \]

Given that \( s = 700 \) feet, we can substitute this value into the formula:

\[ d = \sqrt{2} \times 700 \]

Now, using the provided approximation \( \sqrt{2} \approx 1.4 \), we can substitute this value:

\[ d \approx 1.4 \times 700 \]

Calculating this gives:

\[ d \approx 980 \]

Thus, the approximate length from one corner to the opposite corner of the square park is 980 feet.

So the answer is:

\[ \boxed{980} \text{ feet} \]