I have a retarded maths question that's in my assignment...?

Question

What method is used to work out this question? (please dont give me the answer, just the best way to work it out!);

a guy is an air-traffic contoller who controls the airspace between Cairns and Coolangatta.
Part of his job is to give instructions to pilots as to the path along which they fly.
He has control of a plane flying an altitude of 30 000 feet.
He orders the plane to descend by 3 000 feet at an angle of 30 degrees.

How far (in feet) has the plane travelled from the start of its descent to the time it has descended 3 000 feet?
Draw a diagram to help you.

Okkkk i have no idea how to work this out but like i said before pleeeeeaaaaase dont give me the answer! I only need to know the method of how to work this out.

Thanks guys!

Answer 1

Draw a right-angled triangle with one horizontal side, one vertical side and the hypotenuse at an angle of 30° from the horizontal. The hypotenuse represents the plane's flight path, and the vertical and horizontal lines give us the distance travelled vertically and horizontally.

In this case the vertical distance is 3000 feet, and we want to find the total distance travelled, i.e. the length of the hypotenuse. The vertical distance is opposite the angle of 30°. so that should tell you which trig function you need to use to get the result.

Answer 2

The vertical distance travelled will be 3000 feet at an angle of 30 degrees. A leg of a right-triangle can be measured by taking the hypotenuse multiplied by the sine of the opposite angle. Because the vertical distance is opposite the 30-degree angle, hyp * sin(30) = 3000 feet. If you draw a diagram, you will see that the hypotenuse is the distance flown by the plane. The previous equation can be trivially solved, resulting in distance = 6000 feet.

Answer 3

I am assuming that you know elementary trigonometry (I mean about sine and cosine). So, here the problem can be represented by a right angled triangle which has an angle 30degree and the opposite side is 3000ft., now..
sine (angle) = opposite side / hypotenuse
so, from your problem, sine (30 degree) = 3000ft / hypotenuse
Since the plane actually travels along the hypotenuse, you just solve the eqn to find the length of the path. and BTW sine (30) = 0.5

Answer 4

You need to draw a triangle with 30-60-90 degrees.

The vertical side is 3000 feet.The travelling distance is the horizontal side. You can find using trigonometry.