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 m, find the height of the mast.
Diagram please
Well, if you think about it, this mast is quite the high-wire act. But fear not, my friend! Let's loosen up and have some fun with these wires.
We have a lovely little triangle here, don't we? The base of the triangle is 9m and each wire is 31m long. Now, consider the delightful Pythagorean theorem, which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
So, if we let the height of the mast be "h," we can use Pythagoras to solve this riddle. We have a 9m base and a hypotenuse of 31m. Let's set up a relationship: 9^2 + h^2 = 31^2.
Now, let's solve this equation, shall we? 81 + h^2 = 961. If we subtract 81 from both sides, we get h^2 = 880. Finally, if we take the square root of both sides, we find that h is approximately 29.66m.
Voila! The height of the mast is approximately 29.66 meters. Isn't geometry just a blast?
Is this what GGIS is?
http://www.ggis.hu/
Solve your problem with the Pythagorean Theorem.
I don't know it
I have solve it but I need the diagram to double check my answer
To find the height of the mast, we can use the concept of similar triangles. Let's denote the height of the mast as 'h'.
Given that the wires are attached at points on the level ground 9m from the base of the mast, we can form a right-angled triangle with the base of the triangle representing the distance on the ground and the height of the mast representing the vertical side of the triangle.
Now, consider another triangle formed by extending the top of the mast and connecting it with the ends of the wires. This triangle is similar to the first triangle we formed because the wires are straight and the angle between the wires and the mast is the same at each point.
Since the lengths of the wires are given as 31m, we can establish the following proportion:
h / 9 = (h + 31) / 31
To solve for h, we can cross-multiply:
31h = 9(h + 31)
31h = 9h + 279
31h - 9h = 279
22h = 279
h = 279 / 22
h ≈ 12.68
Therefore, the height of the mast is approximately 12.68m.