TRIGONOMETRY
BY MEGAN ULRICHS
SOLVING SPECIAL RIGHT TRIANGLES
THERE ARE TWO SPECIAL RIGHT TRIANGLES THAT ARE USED OFTEN IN TRIGONOMETRY: THE 30-60-90 AND THE 45-45-90 TRIANGLES. THEY RECEIVE THEIR NAMES FROM THE MEASURES OF THE NAMES FROM THE MEASURES OF THE ANGLES WITHIN THE TRIANGLE.
30-60-90 EXAMPLE:
-STEP 1: USE THE FACT THAT THE SHORT LEG IS HALF THE LENGTH OF THE HYPOTENUSE.
-KEEP IN MIND: TS = 1 UNIT
STEP 2: USE THE TWO KNOWN LENGTHS OF THE RIGHT TRIANGLE AND THE PYTHAGOREAN THEOREM TO FIND THE MISSING MEASUREMENT.
WORK:
THE HYPOTENUSE OF A 30-60-90 IS X, FIND THE LENGTH OF THE LEG.
45-45-90 EXAMPLE:
-STEP 1: USE THE FACT THAT THE LEGS ARE CONGRUENT TO FIND THE LENGTH OF THE OTHER LEG.
-KEEP IN MIND: LM = 4 UNIT
STEP 2: USE THE TWO KNOWN LENGTHS OF THE RIGHT TRIANGLE AND THE PYTHAGOREAN THEOREM TO FIND THE LENGTH OF THE HYPOTONUSE.
WORK:
THE LEG OF A 45-45-90 IS 4 UNITS, FIND THE LENGTH OF THE HYPOTENUSE.