find the length of a right triangle that has a base of 79 meters and a height of 175 meters

Answer 1

To find the hypotenuse of a right triangle when the base and height are known, you can use the Pythagorean theorem, which states:

\[ c = \sqrt{a^2 + b^2} \]

where:

• \( c \) is the length of the hypotenuse,
• \( a \) is the length of one leg (base),
• \( b \) is the length of the other leg (height).

In your case, the base \( a \) is 79 meters and the height \( b \) is 175 meters. Plugging in the values:

\[ c = \sqrt{79^2 + 175^2} \]

Calculating \( 79^2 \) and \( 175^2 \):

\[ 79^2 = 6241 \] \[ 175^2 = 30625 \]

Now add these together:

\[ c = \sqrt{6241 + 30625} \] \[ c = \sqrt{36866} \]

Now, calculate \( \sqrt{36866} \):

\[ c \approx 192.10 \]

So, the length of the hypotenuse is approximately 192.10 meters.

Answer 2

but why is it 156.15

Answer 3

Let's go through the calculation step-by-step again to ensure we arrive at the correct hypotenuse length.

Given:

• Base \( a = 79 \) meters
• Height \( b = 175 \) meters

We need to calculate the hypotenuse \( c \) using the Pythagorean theorem:

\[ c = \sqrt{a^2 + b^2} \]

Calculating \( a^2 \) and \( b^2 \):

\[ a^2 = 79^2 = 6241 \]

\[ b^2 = 175^2 = 30625 \]

Now, add these two results:

\[ a^2 + b^2 = 6241 + 30625 = 36866 \]

Now, we can find \( c \):

\[ c = \sqrt{36866} \]

Calculating \( \sqrt{36866} \):

\[ c \approx 192.10 \text{ meters} \]

It appears that the correct hypotenuse length is approximately 192.10 meters. If you are certain that it should be 156.15 meters, please check the values for base and height that you provided or clarify any additional details about the triangle.