The angle of elevation of the top of a vertical pole from a height 1.5m above a horizontal ground is 40. The foot of the pole is on the same horizontal ground and the point of observation is 20m from pole. Find the height of pole to 3.sp
Draw the diagram. It should be clear that if h is the height of the pole,
(h-1.5)/20 = tan40°
Well, first of all, let me apologize for all the scientific jargon in your question. Let's break it down in simpler terms, just like your favorite bedtime story!
Once upon a time, there was a vertical pole standing tall on the ground, just minding its own business. One fine day, someone with a height of 1.5m above the ground decided to observe the top of the pole.
Now, picture this: The observer was standing 20m away from the pole, looking up at an angle of 40 degrees. Quite the view, I must say! But enough about the observer's sense of entertainment, let's get to the point.
We need to find the height of the pole. Well, I have a funny feeling that we can use a bit of trigonometry here. To be specific, we can use the tangent function.
Tangent is just a fancy way of saying "opposite over adjacent." In this case, the opposite side is the height of the pole (let's call it h) and the adjacent side is the distance from the observer to the pole (which is 20m).
So, according to my trusty clown calculator, we can set up an equation: tan(40) = h/20. Let's do some math!
tan(40) = h/20
h = 20 * tan(40)
And ta-da! Using my super strong clown math skills, the height of the pole turns out to be approximately 17.03m. But hey, don't be too impressed, it's just a clown doing math here!
To find the height of the pole, we can use the tangent function along with the given information.
Let h be the height of the pole.
We have the following information:
- The angle of elevation from the point of observation is 40 degrees.
- The distance from the point of observation to the pole is 20m.
- The point of observation is 1.5m above the horizontal ground.
Using the tangent function, we can set up the following equation:
tan(40) = (h + 1.5) / 20
To find the value of h, we can rearrange the equation:
h + 1.5 = 20 * tan(40)
h + 1.5 = 20 * 0.8391 (rounded to 4 decimal places)
h + 1.5 = 16.782
Subtract 1.5 from both sides:
h = 16.782 - 1.5
h = 15.282
Therefore, the height of the pole is approximately 15.282 meters to 3 significant figures.
To find the height of the pole, we can use trigonometry.
Let's denote the height of the pole as "h."
We are given that the angle of elevation from a height of 1.5m above the ground is 40 degrees. This means that if we draw a right triangle with the ground as the base and the pole as the height, the angle between the ground and the line connecting the top of the pole to the point of observation is 40 degrees.
Since we are given the length of the base (20m) and the length of the opposite side (1.5m + h), we can use the tangent function to find the value of "h."
The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.
In this case, the tangent of 40 degrees is equal to (1.5m + h) / 20m:
tan(40) = (1.5m + h) / 20m
To solve for "h," we can rearrange the equation:
h = (20m) * tan(40) - 1.5m
Now we can plug in the values:
h ≈ (20m) * tan(40) - 1.5m
Using a scientific calculator, the tangent of 40 degrees is approximately 0.839.
h ≈ (20m) * 0.839 - 1.5m
h ≈ 16.78m - 1.5m
h ≈ 15.28m
Therefore, the height of the pole is approximately 15.28 meters.