Question

A surveyor has poles A, B, and C set to form a right triangle with the right angle at B. If the distance from A to B is 35 meters and the distance from B to C is 25 meters, what is the distance from A to C? He can t measure it because there is a deep pond between points A and C.

Answer 1

The question involves using the Pythagorean theorem to calculate the distance across a deep pond in a right triangle. By squaring the known sides and taking the square root of their sum, we find that the distance from A to C is approximately 43 meters.

Step-by-step explanation:

The distance from point A to point C, across the deep pond in a right triangle where A, B, and C form the vertices with a right angle at B, can be found using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, if the distance from A to B is 35 meters (AB=35m) and the distance from B to C is 25 meters (BC=25m), we can calculate AC (the distance from A to C) by the equation:

AB2 + BC2 = AC2

352 + 252 = AC2

1225 + 625 = AC2

1850 = AC2

AC = √1850
AC ≈ 43 meters

Therefore, the distance from point A to point C is approximately 43 meters.

Answer 2

It's about Pythagorean theorem.

AB*AB + BC*BC = AC*AC, so:

35*35 + 25*25 = AC*AC
1225 + 625 = AC*AC
1850 = AC*AC

So AC is a root of 1850, which is ~43 (exactly: 43,01162633521313)

It means that distance between A and C is 43 meters and some milimeters.