A boy 1.5m tall,while standing, views the top of a pole of height 10m at angle of elevation of 40 degrees.How far away is the POLE.?
A boy 1.5m tall, while standing views the top of a pole of height 10m at an angle of elevation of 40 degrees, how far away is the pole
To find the distance to the pole, we can use the tangent function. The tangent of an angle of elevation is equal to the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the pole, which is 10m, and the adjacent side is the distance to the pole that we want to find. The angle of elevation is 40 degrees.
Using the tangent function, we have:
tan(40 degrees) = 10m / x
To find x, we can solve for it algebraically:
x = 10m / tan(40 degrees)
Using a scientific calculator or reference table, we can find that tan(40 degrees) is approximately 0.8391.
Substituting this value back into the equation, we have:
x = 10m / 0.8391
x ≈ 11.92m
Therefore, the pole is approximately 11.92 meters away from the boy.
To determine the distance between the boy and the pole, we can use trigonometry. Specifically, we can use the tangent function.
Let's label the height of the pole as "h" and the distance between the boy and the pole as "d".
From the given information, we know that the height of the pole (h) is 10m and the angle of elevation (θ) is 40 degrees.
Using trigonometry, we can set up the following equation:
tangent(θ) = opposite/adjacent
Since the height of the pole is the opposite side and the distance to the pole is the adjacent side, we can rewrite the equation:
tangent(40 degrees) = 10m/d
Now we can solve for "d" by rearranging the equation:
d = 10m / tangent(40 degrees)
Now we can use a calculator to find the tangent of 40 degrees. After calculating this value, we can substitute it back into the equation to solve for "d".
d = 10m / tangent(40 degrees)
After solving the equation, the calculated value of "d" will give us the distance between the boy and the pole.