an electric post was hit by a lightning and was broken. the broken part makes a right triangle with the ground forming a 20° angle with the other part. the topmost part which is on the ground is 15 meters from the base, how tall is the post before it was hit by a lightning
Assuming the 20° is at the top of the triangle,
let they hypotenus (the fallen over part of the pole) be x
cos20° = 15/x
x = 15/cos20 = 15.96
height of original pole = 15 + 15.96 = 30.96 metres
height = [15 m / tan(20º)] + [15 m / sin(20º)]
Answer
An electric post was hit by a lightning and was broken .the broken part makes a right triangle with the ground forming a 20°angle with the other part the topmost part which is on the ground is 15 feet from the base.how tall is the post before it was hit by the lightning
To find the height of the post before it was hit by lightning, we can use trigonometric ratios involving the given angle and the known side lengths.
Let's label the broken part of the post as "x" and the height of the post before it was broken as "h."
From the given information, we know that the broken part of the post makes a right triangle with the ground and forms a 20° angle.
Now, let's consider the right triangle with the broken part (x) as the base, the height of the post (h) as the vertical side, and the distance from the topmost part to the base (15 meters) as the hypotenuse.
The trigonometric ratio we can use here is the tangent function (tan), which is defined as tangent of an angle equals the opposite side divided by the adjacent side.
In our case:
tan(20°) = h / x
To find "h," we need to eliminate "x" from the equation. We can do this by using the relation between the sides of the triangle.
Using the Pythagorean theorem, we know that:
x^2 + h^2 = 15^2
Now we have two equations:
tan(20°) = h / x
x^2 + h^2 = 15^2
From the first equation, we can solve for "x" by rearranging and isolating it:
x = h / tan(20°)
Substituting this value of "x" into the second equation:
(h / tan(20°))^2 + h^2 = 15^2
Simplifying and rearranging the equation:
h^2 + (h^2 / (tan(20°))^2) = 15^2
h^2 + (h^2 / tan(20°))^2 = 15^2
Now, we can solve this quadratic equation to find the value of "h."