An aircraft at C is spotted by two observers at A and B who are L=1650 feet apart. As the airplane passes over the line joining them, each observer takes a sighting of the angle of elevation to the plane, as indicated in the figure. If a=35 degrees and B=25 degrees, how high is the airplane?
All i have is that 180-35-25=120 degrees im lost now
Drop the altitude from C to P, with height h
AP = h cot35
PB = h cot25
AP+PB = 1650
the elevation of the airplane is approx how many feet? do not round till the final answer then round to two decimal places as needed.
well, geez. I gave you the information:
h(cot35+cot25) = 1650
Now just solve for h!
To solve this problem, we can use trigonometry and the concept of similar triangles. Let me explain the steps to find the height of the airplane:
Step 1: Draw the diagram or visualize the scenario. We have an aircraft flying over a straight line AB, with observers at point A and B. The observers measure the angles of elevation to the plane as a = 35 degrees and B = 25 degrees.
Step 2: Identify the known and unknown quantities. In this case, the known quantities are L (the distance between the observers), a (the angle of elevation measured by observer A), and B (the angle of elevation measured by observer B). The unknown quantity is the height of the airplane (h).
Step 3: Apply trigonometric ratios. In this case, we will use the tangent function.
Tangent of an angle = opposite side / adjacent side.
Step 4: Let's consider the triangle of observer A (triangle ACD in the diagram). Drop a perpendicular line (let's call it DE) from the plane to the line AB. Now we have two similar triangles (triangle ACD and triangle BDE) because the planes of the two triangles are parallel.
Step 5: Use the tangent function to set up equations for each observer:
For observer A:
tan a = DE / AC
For observer B:
tan B = DE / BC
Step 6: Rearrange the equations and substitute values:
tan a = h / AC
tan B = h / BC
Since we are given the distance between observers L = 1650 feet, we can express AC as (AC + BC), which is L. So we have:
tan a = h / (AC + BC)
tan B = h / BC
We can rearrange the equations to isolate h:
h = tan a * (AC + BC)
h = tan B * BC
Step 7: Substitute the given values:
h = tan 35 * (AC + BC)
h = tan 25 * BC
Step 8: Solve the equations simultaneously to find the height of the airplane. You can either use substitution or elimination methods to solve these equations.
Alternatively, if you provide the specific values for AC and BC or L, I can calculate the height of the airplane for you.