Solving Trigonometry word problems

In triangle formulas , the Pythagorean theorem or Pythagoras' theorem a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle in British English). It states:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).Using this,we can find perimeter of a triangle as well.

The theorem can be written as an equation: a² + b² = c²

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.Let's see am example from trigonometry word problems

Question

Two aircraft leave simultaneously from an airport .One flying due north and other due east.The northbound aircraft averages a speed of 630 miles per hour faster than the eastbound aircraft.After 3 hours ,The aircraft are 3510 miles apart.Find the average speed of each aircraft.

Answer


Let the average speed of the east bound aircraft be x mph.

Then the average speed of the north bound aircraft is (x+630)mph

Let the aircraft started from B and C and A are their respective positions after 3 hours.

BC = 3x

and AB = 3(x+630)

From triangle ABC , AC²=AB+BC² (Pythagoras' theorem)

3510²= 9(x+630)²+9x²

1368900 = x²+1260x+396900+x²

2x²+1260x-972000 = 0

x²+630x-486000 = 0

(x+900)(x-270)=0

x= -900,270

But x can't be negative

So x=270 mph


Average speed of the east bound aircraft is 270 mph .Average speed of the north bound aircraft is 900 mph