a rope 10m long from the top of a vertical pole to a point on the ground makes an angle of 23 degrees with the pole how high is it?
Draw a diagram and review your basic trig functions.
h/10 = cos23°
To find the height of the pole, we can use trigonometry. Let's define the height of the pole as "h".
In this scenario, we are given the length of the rope (10m) and the angle it makes with the pole (23 degrees).
We can use the sine function, which relates the opposite side of a right triangle to its hypotenuse:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the height of the pole and the hypotenuse is the length of the rope.
So, we can set up the equation as follows:
sin(23°) = h/10
To solve for "h", we can multiply both sides of the equation by 10:
10 * sin(23°) = h
Using a calculator, we can evaluate sin(23°):
10 * 0.3907 = h
h ≈ 3.907
Therefore, the height of the pole is approximately 3.907 meters.
To determine the height of the pole, we can use the trigonometric relationship between the length of the rope, the angle formed, and the height of the pole.
Let's label the height of the pole as "h" (the value we are trying to find) and the length of the rope as 10m. The angle between the rope and the pole is given as 23 degrees.
Using the trigonometric function "sine" (sin), we know that the sine of an angle is equal to the opposite side divided by the hypotenuse:
sin(angle) = opposite / hypotenuse
In this case, the opposite side is the height of the pole (h), and the hypotenuse is the length of the rope (10m).
So, we can write the equation as:
sin(23 degrees) = h / 10m
Now, we can rearrange the equation to solve for the height of the pole (h):
h = sin(23 degrees) * 10m
To calculate this value, you can use a scientific calculator that has the sine function. Plug in the angle in degrees (23) and multiply it by 10.
h ≈ 3.839 meters (rounded to three decimal places)
Therefore, the height of the pole is approximately 3.839 meters.