from the top of a tower,the angle of depression of boat is 30 degree.if the tower is 20 metre high ,how far is the boat from the frot of the tower
Draw the diagram. You can see that if the distance is x, then
20/x = tan30° = 1/√3
x = 20√3 m
From the top of tower, the angle of depression of a boat is 30degree if the tower is 2ocm high, how far is the boat from the foot of the tower
Using thesame axis, draw the graph of y=2x-3
From the top of a tower the angle of depression of a boat is 30. If the tower is 20 high. How far is the foot of the tower
Well, well, well, it looks like we have a "height"-ened problem here! Let me crunch the numbers and provide you with a hilarious solution.
First things first, we know that the tower is 20 meters high, and the angle of depression is 30 degrees. Now, picture this: the angle of depression is just like when you spot a slice of pizza on the floor and your mood goes "depressed" because it's out of reach. Anyway, back to the problem!
In this case, the angle of depression is the angle between the imaginary line from the top of the tower to the boat and the line parallel to the ground (think of it as a water slide). Now, let's call the distance from the front of the tower to the boat "x" meters.
Since we have this delightful right triangle formed, with the tower's height as one side and the distance to the boat as the hypotenuse, we can use some trigonometry. The tangent of an angle is the opposite side divided by the adjacent side. In this case, the tangent of 30 degrees can be written as:
tan(30 degrees) = 20 / x
Now, was that sailboat rented by a mathematician? Let's find out!
Using our trigonometric magic, we can rearrange the equation to solve for x:
x = 20 / tan(30 degrees)
Now, bring out your calculators (or your amazing mental math skills): tan(30 degrees) is approximately 0.577.
So, x = 20 / 0.577
Calculating that out, we find that the boat is approximately 34.64 meters away from the front of the tower.
Voila! The boat is floating around 34.64 meters away. Just don't forget to bring your sunscreen and your sense of humor with you on the journey!
To find the distance of the boat from the front of the tower, we can use trigonometry. The angle of depression is the angle between the line of sight from the top of the tower to the boat and the horizontal line passing through the top of the tower.
Let's denote the distance from the front of the tower to the boat as "x" (in meters).
In this case, if we draw a right triangle with the tower height (20 meters) as the vertical side and "x" as the horizontal side, the angle of depression (30 degrees) would be the angle opposite the vertical side.
Now we can use the tangent function to relate the angle and the sides of the triangle:
tan(angle) = opposite / adjacent
tan(30°) = 20 / x
Now we need to solve for "x." We can rearrange the equation to isolate "x":
x = 20 / tan(30°)
Using a calculator, we can find the tangent of 30 degrees and calculate:
x = 20 / 0.57735
x = 34.64 meters (approximately)
Therefore, the boat is approximately 34.64 meters away from the front of the tower.