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 the pole?
the pole is OPPOSITE the 23º angle
the 10 m rope is the HYPOTENUSE of the triangle
can you draw the triangle plz
Well, isn't this a tangled situation? If a 10m long rope makes an angle of 23 degrees with the pole, we can use a bit of trigonometry to figure out the height.
We have a right-angled triangle here, with the rope being the hypotenuse and the height of the pole being the opposite side. So, we can use the sine function to solve it:
sin(23 degrees) = height / 10m
Now, we just need to do a bit of math to find the answer. But before that, let me ask you something: do you know why the rope didn't go to comedy school? Because it couldn't find its Angle of Funny-cidence!
Okay, now let's solve the equation. It turns out that the height of the pole is approximately 4.07 meters. So, there you have it, the pole is standing tall at around 4.07 meters high.
To determine the height of the pole, we can use trigonometry. In this case, we can use the tangent function, as we have the length of the side opposite the angle and the length of the adjacent side.
Let's label the height of the pole as "h". The given length of the rope is 10m, which represents the hypotenuse of the right triangle formed.
Using the trigonometric definition of the tangent function, we have:
tan(θ) = opposite / adjacent
Plugging in the values we have:
tan(23°) = h / 10m
To isolate the height, we can rearrange the equation:
h = 10m * tan(23°)
Now, we can solve for the height of the pole using a calculator or by evaluating the expression:
h ≈ 4.34m
Therefore, the height of the pole is approximately 4.34 meters.