From the top of a tower of height 75m, a man sees two goats, both due west of him. If the angles of depression of the two goats are 10 degrees and 17 degrees, calculate the distance between them.
It wants the angle of depression. I , myself, don't understand the question or how to do it. Sorry =(
we are all going to be the next abraham grahambell
the angle of depression from the top of the tower is the same as the angle of elevation from the ground to the top.
So, if the nearer goat is at distance x, and the distance between the goats is d, then
tan 17° = 75/x
tan 10° = 75/(x+d)
So, if we solve for x in both cases, and the equate the two expressions, we get
x = 75/tan17° = 75/tan10° - d
d = 75(cot10°-cot17°) = 180
No problem! I'll be happy to help you understand the question and guide you through the solution.
Let's break down the given information first. We have a tower of height 75m, and a man standing at the top of the tower. The man sees two goats, both due west of him. The angles of depression of the two goats are given as 10 degrees and 17 degrees.
An angle of depression is the angle formed between a horizontal line and the line of sight when looking downwards from an elevated point. In this case, the man is looking downwards from the top of the tower towards the goats.
To find the distance between the two goats, we can use trigonometry. We'll use the tangent function, which relates the angle of depression to the height and distance involved.
Let's consider the first goat with an angle of depression of 10 degrees. Let's call the distance between the man and this goat x1. We can set up the following equation:
tan(10 degrees) = 75 / x1
Similarly, for the second goat with an angle of depression of 17 degrees, let's call the distance between the man and this goat x2:
tan(17 degrees) = 75 / x2
Now, we have two equations with two unknowns (x1 and x2). We can solve this system of equations simultaneously to find the values of x1 and x2.
Once we have the values of x1 and x2, we can find the distance between the two goats by subtracting the distances from the man to each goat:
Distance between the goats = |x1 - x2|, where |x1 - x2| denotes the absolute difference.
To calculate the actual values, you can use a scientific calculator or an online calculator that has trigonometric functions to find the tangent of angles.
I hope this explanation helps you understand how to approach and solve the problem. Let me know if you have any further questions!