to find the distance across a canyon, a surveyor inserts poles a two places o the same side of the canyon as indicated below. using the surveyors measurements given below find the distance across the canyon.
625 and 300
To find the distance across the canyon, we can use the concept of similar triangles. Let's assume that the distance across the canyon is represented by x.
According to the measurements given, the surveyor inserted poles at two places on the same side of the canyon. Let's say the distance between the poles is 625 units, and the distance from one of the poles to the canyon is 300 units.
We can set up a proportion using the measurements:
The ratio of the distance across the canyon (x) to the distance between the poles (625) is equal to the ratio of the distance from one pole to the canyon (300) to the distance between the two poles (625):
x/625 = 300/625
To find the value of x, we can cross-multiply and solve for x:
625 * 300 = x * 625
187,500 = 625x
Dividing both sides of the equation by 625:
x = 187,500 / 625
x = 300
Therefore, the distance across the canyon is 300 units.
You can use this method, known as the concept of similar triangles, to find the distance across the canyon using the measurements provided by the surveyor. Remember to set up a proportion and solve for the unknown variable using cross-multiplication.