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- IN THIS EXAMPLE,
WE WANT TO DETERMINE THE AREA OF THE TRIANGLE
USING THE SINE FUNCTION.
LET'S TAKE A LOOK AT THE AREA OF FORMULA
BEFORE WE DETERMINE THIS AREA.
NORMALLY YOU'RE GIVEN THE AREA OF FORMULA THREE DIFFERENT WAY
AND THAT MIGHT BE A LITTLE BIT CONFUSING.
BUT ON EACH FORMULA, THE MOST IMPORTANT THING TO RECOGNIZE
IS THE RELATIONSHIP BETWEEN THE TWO SIDES AND THE ANGLE.
FOR EXAMPLE IF WE TAKE A LOOK AT THIS FIRST FORMULA,
WE HAVE THE AREA EQUALS 1/2 x "A" x B x SINE C.
SO HERE'S SIDE "A," HERE'S SIDE B AND HERE'S ANGLE C.
ANGLE C IS FORMED BY SIDE A AND SIDE B,
OR WE CAN SAY IT'S THE INCLUDED ANGLE,
AND SO FOR EACH OF THESE FORMULAS
THAT'S THE RELATIONSHIP THAT'S MOST IMPORTANT.
THE ANGLE THAT WE USE MUST BE THE ANGLE
THAT'S FORMED BY THE TWO SIDES OR INCLUDED ANGLE.
IF WE TAKE A LOOK AT THE SECOND FORMULA,
WE HAVE 1/2 B x C x SINE A.
NOTICE HOW SIDE B AND SIDE C FORM ANGLE "A."
AND THE SAME IS TRUE FOR THE THIRD FORMULA,
SIDE "A" AND SIDE C FORM ANGLE B.
SO LOOKING AT OUR EXAMPLE NOW,
IF WE WANT TO DETERMINE THE AREA OF THIS TRIANGLE
AND WE'RE GOING TO USE THIS ANGLE HERE,
THEN WE MUST USE THE LENGTH OF THIS SIDE
AND THE LENGTH OF THIS SIDE IN OUR FORMULA.
SO YOU SHOULDN'T HAVE TO MEMORIZE
ALL THREE OF THESE FORMULAS,
JUST BE AWARE OF THE RELATIONSHIP
BETWEEN THE 2 SIDES AND THE ANGLE USED IN THE FORMULA.
SO FOR THIS EXAMPLE, WE HAVE THE AREA
IS EQUAL TO 1/2 x 12 x 17 x SINE 48 DEGREES.
SO NOW, WE'LL GO TO THE CALCULATOR.
AND BEFORE WE DETERMINE THIS PRODUCT,
WE NEED TO MAKE SURE THAT WE ARE IN DEGREE MODE.
SO PRESS MODE, GO DOWN TO ROW 3,
MAKE SURE THAT DEGREE IS HIGHLIGHTED, PRESS ENTER,
AND NOW WE CAN GO BACK TO THE HOME SCREEN
AND TYPE IN OUR PRODUCT.
WE HAVE 1/2 x 12 x 17 x SINE 48 DEGREES.
SO THE AREA OF THIS TRIANGLE
IS APPROXIMATELY 75.8 SQUARE UNITS.