one mountain is 5000 ft high and can be reached by cable car from another mountain 7000ft away
the other mountain is 3000ft high
what is the lenghtof the cableto link the two mountains
The cable has to rise 2000 feet over a horizontal distance of 5000 feet. The cable would be the hypotenuse of a triangle with those sides, if it were a straight line. However, the cable will have to sag a lot due to its weight and that of the car.
This is not a well thought out problem.
The answer they probably are looking for is
sqrt[(2000)^2 + (5000)^2]
To find the length of the cable needed to link the two mountains, you can use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this scenario, we can consider the distance between the two mountains as the base of the triangle, and the height of the taller mountain as the altitude.
First, let's calculate the altitude of the triangle using the Pythagorean theorem:
altitude^2 = hypotenuse^2 - base^2
altitude^2 = (5000 ft)^2 - (7000 ft)^2
altitude^2 = 25,000,000 ft^2 - 49,000,000 ft^2
altitude^2 = -24,000,000 ft^2
Since we can't take the square root of a negative number in this context, it means there is no triangle that satisfies the given measurements.
Therefore, it is not possible to link these two mountains with a cable of the given measurements.