Two towers 50 meters apart from the top of the shorter tower to the top of the taller tower 43 degree elevation, depression from the top of shorter tower to the bottom of the taller tower is 36 degrees what is the height of each tower?
Draw a diagram.
Review your basic trig functions.
It should be clear that the taller tower has height
50 tan36° + 50 tan43°
the shorter tower's height is just
50 tan36°
To determine the height of each tower, we need to use trigonometry. Let's assign variables to the unknown:
Let h1 be the height of the shorter tower, and h2 be the height of the taller tower.
Now, let's analyze each given piece of information:
1. "Two towers 50 meters apart": This means the distance between the top of the shorter tower and the top of the taller tower is 50 meters.
2. "43 degree elevation from the top of the shorter tower to the top of the taller tower": This implies that we have a right triangle, where the angle between the base (the distance between the two towers) and the height of the shorter tower is 43 degrees. So, we have the base and the angle; we need to find the height. We can use the tangent function for this:
tan(43) = h2 / 50
3. "36 degree depression from the top of the shorter tower to the bottom of the taller tower": Again, we have a right triangle, but this time, the angle is between the base and the difference in height between the two towers. So, we have the base and the angle; we need to find the height. We can again use the tangent function here:
tan(36) = h2 - h1 / 50
Now, we have two equations with two unknowns (h1 and h2). We can solve them simultaneously to find the values.