To find the distance across a canyon, a surveyor inserts poles at two places on the same side of the canyon as indicated below. using the surveyor's measurements given below, find the distance across the canyon. (the answer can be in simplified radical form.)
the measurements are 625 and 300
not enough information
To find the distance across the canyon, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the two other sides.
In this case, let's assume that the distance across the canyon is the hypotenuse of a right triangle, where the two poles represent the other two sides.
Let's label the distance across the canyon as "c" and the lengths of the two sides as "a" and "b". We have the following information:
a = 625
b = 300
According to the Pythagorean theorem, we can write the equation as:
a^2 + b^2 = c^2
Substituting the given values, we have:
625^2 + 300^2 = c^2
Simplifying the equation:
390625 + 90000 = c^2
480625 = c^2
To find the value of c, we need to take the square root of both sides of the equation:
√480625 = √c^2
694.15 ≈ c
Therefore, the distance across the canyon is approximately 694.15 units.