A vertical radio mast is supported by wires attached to its top and to points on the level ground 9m from its base. If each wire is 31m long, find the height of the mast
To find the height of the mast, we can use the Pythagorean theorem. Let's label the height of the mast as 'h' and consider the right-angled triangle formed by the mast, the ground, and one of the wires.
In this triangle, the length of one of the wires is the hypotenuse, and the other two sides are the height of the mast and the distance from the base to the point where the wire is attached to the ground. The length of each wire is given as 31m, and the distance between the base and the point where the wire is attached to the ground is 9m.
Using the Pythagorean theorem, we have:
h^2 + 9^2 = 31^2
Simplifying this equation:
h^2 + 81 = 961
Subtracting 81 from both sides:
h^2 = 880
Taking the square root of both sides:
h = √880
Calculating the square root:
h ≈ 29.664
Therefore, the height of the mast is approximately 29.664 meters.