An airplane is flying at an altitude of 1.8 miles and is 13.7 miles from the runway. Find the angle of depression that the airplane must make to land safely.

Question

NOTE: this assignment is due tomorrow and I have nobody to help me.

I'm in 9th grade algebra II/trig, and we're just starting to do trig. So for work over spring break, we were assigned some geometry work with special right triangles. I don't recall learning about angles of elevation/depression in geometry last year, so if I could have that concept explained in addition to the question, that would be super!

Answer 1

Basically, you are trying to figure the smallest angle inside of a right triangle.

 

In this case, the height of the triangle is 1.8 miles, and the base is 13.7 miles.  From that information, we can calculate the hypotenuse using the Pythagorean theorem c² = a² + b²

 

the hypotenuse, c, will be equal to the square root of a² + b², or the square root of 1.8² + 13.7² = √190.9 ≅ 13.8 miles

 

the height of the triangle will be at the left, the right angle at the vertex of the height and the base. That idea will place the smallest angle at the right of the triangle.

 

you can then use any of the trigonometric functions to figure the angle.

(the sine of an angle = opposite/hypotenuse; the cosine of an angle = adjacent/hypotenuse; the tangent of an angle = opposite/adjacent)

after you make a selection, and do the division, you will have a decimal, and you will be able to find that decimal in a table of trigonometric values, which will give you the angle.