To find out how high the ladder will reach on the building, we can use the Pythagorean theorem. The ladder forms a right triangle with the ground and the side of the building, where:
- The length of the ladder is the hypotenuse (\(c = 10 , \text{m}\)).
- The distance from the base of the building is one leg of the triangle (\(b = 5 , \text{m}\)).
- The height up the building is the other leg of the triangle (\(a\), which we are trying to find).
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Substituting in the values we have:
\[ a^2 + 5^2 = 10^2 \]
This becomes:
\[ a^2 + 25 = 100 \]
Now, subtract 25 from both sides:
\[ a^2 = 100 - 25 \] \[ a^2 = 75 \]
Now, take the square root of both sides:
\[ a = \sqrt{75} \] \[ a = 5\sqrt{3} \]
Since \( \sqrt{75} \) is approximately 8.7 m, the ladder will reach approximately 8.7 m up the building.
So the correct response would be:
"5 squared plus x squared is equal to 10 squared; x = √75 m, which is an irrational number and would be estimated to be 8.7 m."