a vertical radio mast is supported by wires attached to its top and to points on level ground 9 meter from its base. if each wire is 31 metre long,find the height of the mast
h^2 = 31^2 - 9^2
Damilola
Well, this situation sounds like it would be quite unbalanced, just like my sense of fashion. Let's see if we can figure it out with a little bit of humor and some math.
Since the wires are attached to the top of the mast and to points on the ground 9 meters away from the base, we have ourselves a lovely right triangle. Picture it: the mast is the vertical side, the wires are the hypotenuse, and the distance from the base to the points on the ground is the horizontal side. So far, so good?
Now, we know that each wire is 31 meters long. That means the hypotenuse of our triangle is a delightful 31 meters, the length of a whale's belly button lint collection.
But how do we find the height of the mast, you ask? Well, in this right triangle, we can use a favorite mathematical tool called the Pythagorean theorem. It says that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. So in this case, we have:
(Height of mast)^2 + (Horizontal distance)^2 = (Length of wire)^2
Using some fancy algebraic dancing, we can rearrange this equation to solve for the height of the mast. Plugging in the values we know, we get:
(Height of mast)^2 = (Length of wire)^2 - (Horizontal distance)^2
(Height of mast)^2 = 31^2 - 9^2
Now, we just need to do some simple calculations to find the answer:
(Height of mast)^2 = 961 - 81
(Height of mast)^2 = 880
Taking the square root of both sides, we find:
Height of mast ≈ √880
Height of mast ≈ 29.66
So, the height of the mast is approximately 29.66 meters. Who knew math could be so funny? Now, go on and tell this joke to all your friends... or maybe just enjoy a nice laugh all by yourself!
To find the height of the mast, we can use the property of a right-angled triangle formed by the mast, the ground, and one of the supporting wires.
Let's label the height of the mast as 'h' and the distance from the base of the mast to the point where the wire is attached as 'x'.
According to the given information:
- Each wire is 31 meters long.
- The points on the ground where the wires are attached are 9 meters away from the base of the mast.
Using Pythagoras' theorem, we have the following equation:
x^2 + h^2 = 31^2
Since we know that x = 9, we can substitute this value into the equation:
9^2 + h^2 = 31^2
Simplifying:
81 + h^2 = 961
Subtracting 81 from both sides:
h^2 = 880
To isolate h, take the square root of both sides:
sqrt(h^2) = sqrt(880)
h = sqrt(880)
Calculating the square root of 880:
h ≈ 29.664
So, the height of the mast is approximately 29.664 meters.
To find the height of the mast, we can use the Pythagorean theorem.
Let's consider the right-angled triangle that is formed by the mast, the wires, and the ground. The length of each wire is given as 31 meters, and the distance between each wire attachment point on the ground is also given as 9 meters.
Let's label the height of the mast as 'h.'
Using the Pythagorean theorem, we have:
(9)^2 + h^2 = (31)^2
Simplifying the equation:
81 + h^2 = 961
Subtracting 81 from both sides of the equation:
h^2 = 880
Taking the square root of both sides, we get:
h ≈ 29.664
Therefore, the height of the mast is approximately 29.664 meters.