- WE WANT TO SOLVE THE RIGHT TRIANGLE
GIVEN THE LENGTH OF SIDE B IS EIGHT UNITS,
AND THE MEASURE OF ANGLE B IS 38 DEGREES.
SO IF ANGLE B IS 38 DEGREES, SIDE B IS OPPOSITE THIS ANGLE,
TO THIS WOULD BE SIDE B.
WE KNOW THIS LENGTH IS EIGHT UNITS.
SO IF THIS IS ANGLE A, THEN THIS WOULD BE SIDE A.
IF THIS IS ANGLE C, THIS WOULD BE SIDE C.
LET'S START BY FINDING THE MEASURE OF ANGLE A.
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 HAVE A SUM OF 90 DEGREES,
WHICH MEANS THE MEASURE OF ANGLE A
MUST BE EQUAL TO 90 DEGREES - 38 DEGREES,
WHICH IS EQUAL TO 52 DEGREES.
NOW, WE NEED TO FIND THE LENGTH OF SIDE A
AND THE LENGTH OF SIDE C.
TO DO THIS WE'LL HAVE TO USE A TRIG EQUATION.
SO THE FIRST WE HAVE TO DECIDE
WHICH ANGLE WE WANT TO USE IN THE TRIG EQUATION.
LET'S SAY THAT WE WANT TO USE ANGLE A.
WE KNOW WE ALSO HAVE TO USE THE LENGTH OF SIDE B
BECAUSE WE CAN ONLY HAVE ONE UNKNOWN IN OUR EQUATION.
SO IF WE WANT TO USE THIS ANGLE AND THIS SIDE,
LET'S SAY WE WANT TO FIND THE LENGTH OF SIDE C.
WELL, B IS THE ADJACENT SIDE TO ANGLE A,
AND C IS THE HYPOTENUSE.
AND SINCE THE COSINE FUNCTION INVOLVES THE ADJACENT SIDE
AND THE HYPOTENUSE SIDE OF A RIGHT TRIANGLE,
WE KNOW WE HAVE TO USE THE COSINE OF 52 DEGREES
IN OUR EQUATION.
SO OUR EQUATION WILL BE THE COSINE OF 52 DEGREES
MUST EQUATION THE RATIO OF THE ADJACENT SIDE OF THE HYPOTENUSE
OR EIGHT OVER C.
NOW, TO CLEAR THIS FRACTION WE'LL MULTIPLY BOTH SIDES BY C.
SO LET'S SIMPLIFY OUT.
SO WE'LL HAVE C x COSINE 52 DEGREES MUST EQUAL EIGHT.
AND NOW WE'LL DIVIDE BOTH SIGNS BY A COSINE 52 DEGREES.
SO C = THIS QUOTIENT HERE.
SO NOW WE'LL GO TO THE CALCULATOR.
ONE OF THE MOST IMPORTANT THINGS TO DO IS RECOGNIZE
THAT WE HAVE TO HAVE OUR CALCULATOR IN DEGREE MODE.
SO I'LL PRESS THE MODE KEY.
NOTICE HOW IN MY THIRD ROW THE DEGREE FEATURE IS HIGHLIGHTED.
SO I AM IN THE CORRECT MODE.
IF I GO BACK TO THE HOME SCREEN,
AND NOW I WANT TO FIND THIS QUOTIENT HERE.
EIGHT DIVIDED BY COSINE 52 DEGREES.
IF WE ROUND TO THE NEAREST TENTH THIS WOULD BE 13.0.
NOW WE NEED TO FIND THE LENGTH OF SIDE A.
NOW THAT WE KNOW THE LENGTH 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.
SO LET'S GO AHEAD AND USE ANGLE A AGAIN.
WE KNOW WE'RE GOING TO USE SIDE A BECAUSE THAT'S THE UNKNOWN.
NOW, WE HAVE THE OPTION OF USING SIDE C,
WHICH IS APPROXIMATELY 13.0, OR SIDE B,
WHICH WE KNOW IS EXACTLY EIGHT UNITS.
I'M GOING TO USE SIDE B
BECAUSE I KNOW THIS IS THE EXACT VALUE.
IF I USE INVENTED VALUE OF SIDE C
THERE WILL BE MORE OF AN ERROR.
REFERENCING ANGLE A,
NOTICE HOW THE SIDE A IS THE OPPOSITE SIDE,
AND SIDE B IS THE ADJACENT SIDE.
THE TRIG FUNCTION VALUE THAT USES THE OPPOSITE SIDE
AND ADJACENT SIDE OF A RIGHT TRIANGLE IS TANGENT
WHICH MEANS NOW WE'LL HAVE THE EQUATION TANGENT 52 DEGREES
MUST EQUAL A DIVIDED BY EIGHT.
NOTICE IN THIS EQUATION WE CAN SOLVE FOR A IN ONE STEP.
WE CAN MULTIPLY BOTH SIDES OF THE EQUATION BY EIGHT
TO DETERMINE THE VALUE OF A.
NOTICE HERE THIS SIMPLIFIES OUT.
SO A IS APPROXIMATELY EQUAL TO THIS PRODUCT HERE,
8 x TANGENT 52 DEGREES.
SO 8 TANGENT 52 DEGREES.
SO THE LENGTH OF SIDE A TO THE NEAREST TENTH
WOULD BE APPROXIMATELY 10.2 UNITS.
OKAY. I HOPE YOU FOUND THIS HELPFUL.