cASEY SIGHTS THE TOP OF AN 84 FOOT TALL LIGHTHOUSE AT AN ANGLE OF ELEVATION OF 58 DEGREE. IF CASEY IS 6 FEET TALL, HOW FAR IS HE STANDING FROM THE BASE OF THE LIGHTHOUSE.
I DO NOT UNDERSTAND WHAT IS ANGLE OF ELEVATION CAN YOU SHOW ME AN EXAMPLE PLEASE THANK YOU.
48.7
draw a diagram. If you label
T = top of lighthouse
B = base of lighthouse
C = Casey
then the angle of elevation is the angle BCT
That is, 0° is a horizontal line of sight, meaning that he has to look up at an angle of 58° to see the top of the lighthouse.
So, using you basic trig functions, and assuming that Casey's eyes are at the top of his head, then the part of the lighthouse above Nick's eyes (84-6 feet), sets up our triangle
(84-6)/x = tan 58°
Now just solve for x, the distance of Casey from B.
tan 58 78/x - 78/tan 58
Sure, I can explain what angle of elevation is and also help you solve the given problem.
When we talk about the angle of elevation, we are referring to the angle between a horizontal line (ground level) and a line of sight that points upward. It is the angle at which we need to look up (or elevate our line of sight) in order to see an object that is above our eye level.
Here's an example to help illustrate this:
Imagine standing on the ground and looking up at a tall building. If you tilt your head upward to look at the top of the building, the angle between the horizontal ground line and your line of sight is the angle of elevation.
Now, let's solve the problem given:
Casey sights the top of an 84-foot tall lighthouse at an angle of elevation of 58 degrees. Casey's height is 6 feet. We need to find the distance between Casey and the base of the lighthouse.
To solve this, we can create a right-angled triangle. The height of the lighthouse represents the opposite side, and the distance between Casey and the base of the lighthouse represents the adjacent side. The angle of elevation is given as 58 degrees.
Since we have the opposite (84 feet) and the angle of elevation, we can use the tangent function to find the adjacent side.
Tangent function: tan(angle) = opposite / adjacent
In this case, we can write the equation as:
tan(58) = 84 / adjacent
To find the adjacent side, we rearrange the equation:
adjacent = 84 / tan(58)
Using a calculator, we can find that tan(58) is approximately 1.6643.
So, the equation becomes:
adjacent = 84 / 1.6643
Calculating this, we find that the adjacent side is approximately 50.48 feet.
Therefore, Casey is standing approximately 50.48 feet away from the base of the lighthouse.
I hope this explanation helps! If you have any further questions, please let me know.