Altitude A plane is observed approaching your home and you assume its speed is 550 miles per hour. The angle of elevation to the plane is at 16 degrees at one time and 57 degrees one minute later. Approximate the altitude of the plane.
From what follows, I am assuming that the edit (in
red above) is correct.
I have already drawn a triangle with an angle of elevation of 16 degrees and from the same point as that angle, an angle with an elevation of 57 degrees. I drew a horizontal line connecting the tops of the line from the second angle to the top of the first triangle and labeled that side length 9.166666 miles per second. Where do I go from here?
I'm not sure what your picture is. Let's start with some labelling:
The ground will be an horizontal line. Let's call "your" position "Y", and draw a dot near the right-hand end of this line.
The plane's path is presumed to be level, so draw another horizontal line, an inch or so (or a couple of centimeters) above the first line.
Draw a dot, near the left-hand end of the second line, for the "first" observation. Label this point as "F", and draw the line of sight, YF. Below the point F, label another point "G" on the first line (which is the "ground"). Below the point S, label another point "H" on the ground. We'll use these points later.
Draw another dot, maybe around the middle of the second line, for the "second" observation. Label this point as "S", and draw the line of sight, YS.
From Y, draw a vertical line up to the second line. This is the height, "h", of the plane above the ground.
You are given that the plane travels 550 miles in one hour. Then how many miles does it cover in one minute? (Hint: Divide. Leave your answer in exact form; do not use a decimal approximation.) Label the line segment FS with this value.
Label the angle GYF as "16"; label the angle GYS as "57". Draw the segment FG. Note that the length of FG is equal to the value for h, which is what they're wanting. Draw the segment SH, which also has a length equal to the value of h. Label the segment GH with the value you have given to the segment FS, which obviously has the same length. Label the rest of GY (being the segment HY) with length "x".
You now have two triangles. Triangle GYF has base |FS| + x, height h, and a base angle measuring 16. Triangle HYS has base x, height h, and a base angle measuring 57. Solve the system for the value of h. (You don't need to find the value of x.)
