Solve a Right Triangle Given an Angle and a Leg

Solve a Right Triangle Given an Angle and a Leg


– 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.  

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