Answer:
The distance is 5.20m
Step-by-step explanation:
Here, we want to get the height of the ladder
To get this, we need to understand that we have a right triangle, with the base of the triangle as 3 m, the angle at the downward part is 60, and we want to get the height of the triangle
The angle here faces the height we want to calculate
This height is known as the opposite
What we have is the adjacent
Now, the trigonometric identity that relates the opposite and the adjacent is the tan
The tangent of an angle is the ratio of the opposite to the adjacent
Mathematically;
tan 60 = h/3
h = 3 tan 60
h = 5.20 m
The ladder is at a height of 5.20 m above the ground
Answer:
![\frac{dAB}{dt}=340 mil/h](https://tex.z-dn.net/?f=%5Cfrac%7BdAB%7D%7Bdt%7D%3D340%20mil%2Fh)
Step-by-step explanation:
The change of distance over time of the plain A is 300 mi/hour and 200 mi/hour for plane B. O is the point of the airport.
So, the distance from A to O AO = 90 miles and BO = 120 miles.
Now, we have a right triangle here. We can use the Pythagorean theorem, so the distance between the planes will be:
(1)
![AB =\sqrt{AO^{2}+BO^{2}}=](https://tex.z-dn.net/?f=AB%20%3D%5Csqrt%7BAO%5E%7B2%7D%2BBO%5E%7B2%7D%7D%3D)
![AB =\sqrt{90^{2}+120^{2}}=150 miles](https://tex.z-dn.net/?f=AB%20%3D%5Csqrt%7B90%5E%7B2%7D%2B120%5E%7B2%7D%7D%3D150%20miles)
If we take the derivative of the equation (1) we could find the change of the distance between planes.
![2*150\frac{dAB}{dt}=2*90*300+2*120*200=102000 mil/h](https://tex.z-dn.net/?f=2%2A150%5Cfrac%7BdAB%7D%7Bdt%7D%3D2%2A90%2A300%2B2%2A120%2A200%3D102000%20mil%2Fh)
![\frac{dAB}{dt}=\frac{102000}{150*2}](https://tex.z-dn.net/?f=%5Cfrac%7BdAB%7D%7Bdt%7D%3D%5Cfrac%7B102000%7D%7B150%2A2%7D)
Finally,
![\frac{dAB}{dt}=340 mil/h](https://tex.z-dn.net/?f=%5Cfrac%7BdAB%7D%7Bdt%7D%3D340%20mil%2Fh)
I hope it helps you!
It's hard to type a table into these little boxes. Could you possibly draw the table on paper and share an image of the table here?
This is called a "contingency table" and is often associated with "dependent probability."