Mr. Bennet is standing on a tower 50 ft. Above the ground looks down and spots Joe. The angle of depression to Joe is 35 degrees.How far away from the base of the tower is Joe?
I am not sure on how to figure out the angle of depression, any sort of help would be very beneficial for me and others I am sure who don't understand this and are afraid to ask help. Thanks :)
The angle of depression is the "downward" angle. So originally in your diagram it is outside the triangle at the top. BUT when you use parallel line theorems you see that the Angle of Depressison has the same value as the ANgle of Elevation (which is inside the triangle at the bottom) So in this case at Joe's feet : )
Ms Pi 3.14159265358979323,
I am very sorry to say, but in my mind what you are saying kind of doesn't make very much sense to me. Is there another way you could say it that would maybe make sense to me?
DRAW IT !!!!
Tower, horizontal line through top of tower to over Joe,
parallel horizontal line through bottom of tower to Joe
slant line down
Think about parallel lines where they intersect with a crossing line.
The angle of depression is equal to the angle of elevation.
So... the 35 degrees goes in the bottom corner of the triangle beside Joe.
FYI
you also know that opposite to your 35 degrees is the side of the triangle that has the 50 feet. So you are trying to find the ADJACENT side, when you have the OPPOSITE side... so you will be using the TANGENT ratio : )
To solve this problem, we can use trigonometry. The angle of depression is the angle formed between the horizontal line and the line of sight from the observer (Mr. Bennet) to the object being observed (Joe).
In this case, Mr. Bennet is standing on a tower, and the angle of depression to Joe is 35 degrees. We can consider the vertical line connecting Mr. Bennet's eyes and the ground as perpendicular to the ground.
Drawing a diagram can help us visualize the scenario. Let's represent the base of the tower as point A, Mr. Bennet's position as point B, and Joe's position as point C.
To find the distance from Joe to the base of the tower (BC), we need to use tangent, which is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
In this case, BC is the opposite side and AB is the adjacent side. Using the tangent function, we have:
tan(angle of depression) = BC / AB
Or
tan(35 degrees) = BC / AB
Now, we can solve for BC by rearranging the equation:
BC = AB * tan(35 degrees)
Since we know that Mr. Bennet is standing on a tower 50 ft above the ground, AB is 50 ft.
BC = 50 ft * tan(35 degrees) ≈ 29.09 ft
Therefore, Joe is approximately 29.09 feet away from the base of the tower.