- WE WANT TO SOLVE THE RIGHT TRIANGLE
GIVEN THE LENGTH OF SIDE C = 12,
AND THE MEASURE OF ANGLE A IS 40 DEGREES.
LET'S START BY LABELING EACH SIDE OF OUR RIGHT TRIANGLE.
IF THIS IS ANGLE A,
THEN SIDE A IS OPPOSITE THIS ANGLE.
SO THIS WOULD BE SIDE A.
WHERE THIS IS ANGLE B,
THEN THE OPPOSITE SIDE IS SIDE B, OR THIS SIDE.
THIS IS ANGLE C,
THEN THE OPPOSITE SIDE OF THE HYPOTENUSE WOULD BE SIDE C.
SO WE'RE GIVEN THE LENGTH OF SIDE C,
OR THE HYPOTENUSE IS 12 UNITS.
AND WE'RE ALSO TOLD THE MEASURE OF ANGLE A IS 40 DEGREES.
LET'S START BY DETERMINING THE MEASURE OF ANGLE B.
WELL, WE KNOW THE SUM OF THE INTERIOR ANGLES
OF A TRIANGLE MUST BE 180 DEGREES.
BUT IT'S ALSO TRUE THAT THE TWO ACUTE ANGLES
MUST BE COMPLIMENTARY OR HAVE A SUM OF 90,
WHICH MEANS THE MEASURE OF ANGLE B
MUST BE EQUAL TO 90 DEGREES - 40 DEGREES.
SO THE MEASURE OF ANGLE B = 50 DEGREES.
NOW WE'RE LEFT TO FIND THE LENGTH OF SIDE A
AND THE LENGTH OF SIDE B.
TO DO THIS WE'LL HAVE TO USE A TRIG EQUATION.
SO LETS FIRST DECIDE WHICH ANGLE WE'RE GOING TO USE.
LET'S SAY WE'RE GOING TO USE ANGLE A.
AND WE WANT TO FIND THE LENGTH OF SIDE A.
WELL, WE KNOW WE HAVE TO USE THE LENGTH OF SIDE C
BECAUSE WE KNOW THE VALUE OF C,
AND WE CAN ONLY HAVE ONE UNKNOWN IN OUR TRIG EQUATION.
SO NOTICE THAT A IS THE OPPOSITE SIDE OF ANGLE A
AND C IS THE HYPOTENUSE.
AND SINCE THE SIN FUNCTION INVOLVES THE OPPOSITE SIDE
AND HYPOTENUSE OF A RIGHT TRIANGLE,
WE KNOW WE HAVE TO USE THE SIN FUNCTION IN OUR TRIG EQUATION.
SO OUR TRIG EQUATION IS GOING TO BE THE SIN OF 40 DEGREES
MUST BE EQUAL TO THE RATIO OF THE OPPOSITE SIDE
TO THE HYPOTENUSE, OR IN THIS CASE A DIVIDED BY 12.
AND NOW WE NEED TO SOLVE THIS EQUATION FOR A.
SO WE'LL MULTIPLY BOTH SIDES BY 12.
SO THE RIGHT SIDE SIMPLIFIES TO A.
SO A IS EQUAL TO THIS PRODUCT HERE,
WHICH WE WILL APPROXIMATE USING THE CALCULATOR.
ONE OF THE MOST IMPORTANT THINGS WE NEED TO DO IS TO MAKE SURE
THAT OUR CALCULATOR IS IN DEGREE MODE.
SO I'M GOING TO PRESS THE MODE KEY.
NOTICE DEGREE IS HIGHLIGHTED, SO WE ARE IN DEGREE MODE.
SO NOW FROM THE HOME SCREEN WE'LL APPROXIMATE THIS PRODUCT.
12 x SIN 40 DEGREES.
TO THE NEAREST TENTH THIS WOULD BE APPROXIMATELY 7.7 UNITS,
IS THE LENGTH OF SIDE A.
NOW WE'RE LEFT TO DETERMINE THE LENGTH OF SIDE B.
BECAUSE NOW WE HAVE THE LENGTHS OF TWO SIDES
OF THE RIGHT TRIANGLE,
WE COULD USE THE PYTHAGOREAN THEOREM,
BUT I'M GOING TO GO AHEAD AND USE ANOTHER TRIG EQUATION.
LET'S GO AHEAD AND USE ANGLE A AGAIN.
WE KNOW WE HAVE TO USE SIDE B,
BUT NOW WE HAVE A CHOICE TO USE SIDE A OR SIDE C.
I WOULD RECOMMEND USING SIDE C
BECAUSE WE KNOW THIS EXACTLY 12 UNITS.
SIDE A HAS BEEN ROUNDED.
SO IF WE USE SIDE A THERE WILL BE MORE OF AN ERROR.
SO WE'LL USE SIDE C.
SO REFERENCING ANGLE A,
NOTICE THAT SIDE B IS THE ADJACENT SIDE,
AND SIDE C IS THE HYPOTENUSE.
AND SINCE THE COSINE FUNCTION VALUE INVERSE THE ADJACENT SIDE
AND HYPOTENUSE OF A RIGHT TRIANGLE,
WE HAVE TO USE COSINE IN OUR TRIG EQUATION.
WE'LL HAVE THE COSINE OF 40 DEGREES = B DIVIDED BY 12.
AND NOW TO SOLVE FOR B WE'LL MULTIPLY BOTH SIDES BY 12.
THE LENGTH OF SIDE B = THIS PRODUCT HERE,
WHICH WE'RE APPROXIMATE ON THE CALCULATOR.
SO NOW WE HAVE 12 x COSINE 40 DEGREES.
SO THE LENGTH OF SIDE B IS APPROXIMATELY 9.2 UNITS.
AND NOW WE HAVE ALL OF THE INFORMATION WE'RE ASKED TO FIND.