A mini toy helicopter ascends 50 feet vertically, then flies horizontally 200 feet. Find the angle of elevation to the helicopter now as seen by an observer at the takeoff point.

10.036

Step-by-step explanation:

Remark

Draw a triangle starting with a vertical line that goes from (0,0) to (0,50).

At the point (0,50) draw a horizontal line to (200,50)

Join the point (200,50) to (0,0)

What you have is an upside down right triangle. At the point (200,50) your job is to find the angle at the vertex point.

That angle is the same as the angle of elevation.

The horizontal line is 200 feet.

The vertical line is 50 feet

Formula

Tan(angle elevation) = o/a = 50/200 = 1/4 = 0.25

Solution

tan-1(0.25) = 14.036

Conclusion

The reason you use the top angle is because you only need to do one calculation. It gives the angle of elevation because the x axis and the 200 feet are parallel. The angles are in a z formation.  so the angle you found and the angle of elevation are the 2 angles defined by the z.

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation: