An electric post was broken by a strong typhoon.It formed a right triangle with the ground.If a broken part makes an angle of 25 degrees with the other part,and the topmost part of the post which is post which is on the ground is 40 ft from the base,how tall was the post?
Well, isn't that electrifying! Let's solve this puzzle.
We have a right triangle formed by the broken electric post, and we know the angle between the two parts is 25 degrees. The adjacent side to this angle is the part of the post on the ground, which measures 40 ft.
Now, to find the height of the post, we need to determine the length of the opposite side. Since we're dealing with a right triangle, we can use trigonometry. Specifically, the tangent function is what we need here.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. So, we can use the tangent of 25 degrees to find the height.
Let's do the math: tan(25°) = height / 40
Now, solving for the height, we get:
height = tan(25°) * 40
Using a trusty calculator, we find that tan(25°) is approximately 0.4663. Plugging it into the equation, we get:
height ≈ 0.4663 * 40 ≈ 18.65 ft
So, the height of the electric post is approximately 18.65 feet. Keep an eye out for any more humorous questions!
To solve this problem, we can use trigonometric ratios. Let's call the height of the post "h". We have a right triangle formed by the broken part of the post (adjacent side), the remaining part of the post (opposite side), and the horizontal distance from the top of the post to the base (hypotenuse).
We know that the broken part of the post makes an angle of 25 degrees with the remaining part. Therefore, the angle between the height of the post and the horizontal distance is 90 - 25 = 65 degrees.
Using the information given, we can set up the trigonometric equation:
tan(65) = h / 40
Solving this equation for h, we get:
h = 40 * tan(65)
Calculating this using a calculator, we find:
h ≈ 92.2 ft
Therefore, the height of the post is approximately 92.2 feet.
To find the height of the post, we can use trigonometry.
Let's label the parts of the triangle:
- The broken part of the post is the side opposite to the 25-degree angle.
- The other part of the post is the side adjacent to the 25-degree angle.
- The base of the triangle is the side opposite to the right angle, which is also the distance between the topmost part of the post and the base on the ground.
Now, we can use the tangent function to find the height of the post:
tan(25 degrees) = opposite/adjacent
In this case, the opposite side is the height of the post, and the adjacent side is the distance between the topmost part of the post and the base on the ground.
Let's represent the height of the post as "h":
tan(25 degrees) = h/40 ft
To solve for "h", we can multiply both sides of the equation by 40 ft:
tan(25 degrees) * 40 ft = h
Using a calculator, we can find the value of tan(25 degrees) to be approximately 0.4663:
0.4663 * 40 ft = h
So, the height of the post is approximately:
h ≈ 18.65 ft
Therefore, the post is approximately 18.65 feet tall.
Y = 40 Ft = Hor. side = The side opposite the 25-Deg angle.
X = Ver. side.
r = hyp.
sin25 = Y/r = 40 / r.
r = 40 / sin25 = 94.6 Ft.
tan25 = Y/X = 40 / X.
X = 40 / tan25 = 85.8 Ft.
h = X + r = 85.8 + 94.6 = 180.4 Ft.