From two points A and B, 43m apart and on the same horizontal line with the foot C of an electric pole, the angles of elevation of the top of the pole are 24 degree and 37 degree respectively. Find the heights of the pole
I assume A and B are on the same side of the pole
tan 37 = h/b
tan 24 = h/(b+43)
b = h/tan 37
tan 24 = h/ (h/tan 37 + 43)
.445 = h/ (1.33 h + 43)
.5905 h + 19.1 = h
.4095 h = 19.1
h = 46.6
2a+3a=5a²
Mathematics Multiples and common multiples Inside-out maths
Well, this seems like a high-wire situation! Let's break it down.
First, we can use some trigonometry to find the height of the pole.
Let's call the height of the pole "h".
From point A, the angle of elevation to the top of the pole is 24 degrees. So, we can set up the equation:
tan(24) = h / AC
Where AC is the distance from point A to the foot of the pole.
Similarly, from point B, the angle of elevation is 37 degrees. So, we can set up another equation:
tan(37) = h / BC
Where BC is the distance from point B to the foot of the pole.
Since AC and BC are the same distance and given as 43m, we can say:
AC = BC = 43m
Now, we can substitute these values into the equations:
tan(24) = h / 43
tan(37) = h / 43
Using a scientific calculator, we can find that:
h = 43 * tan(24) = 18.13m (approximately)
h = 43 * tan(37) = 28.11m (approximately)
So, it seems the height of the pole is about 18.13m from point A and 28.11m from point B.
Looks like the pole is reaching for new heights, literally!
To find the height of the pole, we can use trigonometric ratios and the given information about the angles of elevation.
Let's label the height of the pole as 'h'.
From the point A, the angle of elevation to the top of the pole is 24 degrees. This means that we can set up the following trigonometric equation:
tan(24 degrees) = h / AB,
where AB represents the distance between points A and B, which is 43m.
Using a calculator, we can find that tan(24 degrees) is approximately 0.44504187.
Therefore, the equation becomes:
0.44504187 = h / 43.
To find the value of h, we can rearrange the equation:
h = 0.44504187 * 43.
Evaluating this expression, we find that h is approximately 19.142m.
So, the height of the pole is approximately 19.142m.
Now, let's consider the point B. The angle of elevation to the top of the pole from B is 37 degrees. We can set up the following similar trigonometric equation:
tan(37 degrees) = h / AB.
Using a calculator, we find that tan(37 degrees) is approximately 0.75355405.
Therefore, the equation becomes:
0.75355405 = h / 43.
Rearranging the equation:
h = 0.75355405 * 43.
Evaluating this expression, we find that h is approximately 32.417m.
So, the height of the pole is approximately 32.417m from point B.
Therefore, the height of the pole is approximately 19.142m from point A and 32.417m from point B.
If A and B are on opposite sides of the pole, then
h cot 37° + h cot 24° = 43