Tip:
Highlight text to annotate it
X
- WE WANT TO SOLVE THIS TRIANGLE
GIVEN THE LENGTH OF ONE OF THE SIDES AND THE MEASURE
OF TWO OF THE ANGLES.
TO KEEP THINGS ORGANIZED, LET'S GO AHEAD AND LABEL
THE VERTICES AND THE SIDES.
SO LET'S CALL THIS VERTEX "A," B AND C, THEREFORE SIDE "A"
IS OPPOSITE ANGLE "A," SIDE B IS OPPOSITE ANGLE B,
AND SIDE C IS OPPOSITE ANGLE C.
RIGHT AWAY IF WE'RE GIVEN 2 INTERIOR ANGLES OF A TRIANGLE,
WE SHOULD BE ABLE TO DETERMINE THE THIRD ANGLE,
BECAUSE WE KNOW THE SUM OF THE INTERIOR ANGLES
MUST BE 180 DEGREES.
SO THE MEASURE OF ANGLE B WOULD BE EQUAL
TO 180 DEGREES - 132 DEGREES - 18 DEGREES.
SO THE MEASURE OF ANGLE B IS GOING TO BE EQUAL
TO 30 DEGREES.
NOW IF WE TAKE A LOOK AT THE INFORMATION THAT WE HAVE,
NOTICE THAT WE HAVE THE MEASURE OF AN ANGLE AND THE LENGTH
OF THE OPPOSITE SIDE AND THEREFORE WE CAN SOLVE
THIS TRIANGLE USING THE LAW OF SINES.
SO LET'S GO AHEAD AND START BY DETERMINING THE LENGTH
OF SIDE C.
SO IF WE WANT TO DETERMINE SIDE C, WE'LL HAVE TO HAVE
THE SINE OF ANGLE C DIVIDED BY C.
SO WE'LL HAVE THE SINE OF 132 DEGREES DIVIDED BY C
MUST EQUAL THE SINE OF 18 DEGREES DIVIDED BY 7.
REMEMBER TO SET THIS UP, WE CAN ONLY HAVE ONE
UNKNOWN VALUE AND HERE THE ONLY UNKNOWN IS C.
AND NOW, WE CAN CROSS MULTIPLY AND SOLVE FOR C.
SO WE'LL HAVE C SINE 18 DEGREES MUST EQUAL 7 x SINE 132 DEGREES.
SO NOW, WE'LL DIVIDE BOTH SIDES BY SINE 18 DEGREES,
AND THIS QUOTIENT WILL GIVE US THE LENGTH OF SIDE C.
LET'S MAKE SURE THAT WE'RE IN DEGREE MODE,
AND WE ARE.
SO THE NUMERATOR IS GOING TO BE 7 SINE 132 DEGREES.
WE'RE GOING TO DIVIDE THIS BY SINE 18 DEGREES.
SO THE LENGTH OF SIDE C IS APPROXIMATELY 16.8,
AND THIS SHOULD BE METERS.
AND NOW, WE'RE LEFT TO DETERMINE THE LENGTH OF SIDE B.
SO WE'LL GO AHEAD AND SET UP A SIMILAR PROPORTION.
BUT SINCE WE WANT TO DETERMINE THE LENGTH OF SIDE B,
WE'RE GOING TO HAVE THE SINE OF ANGLE B
DIVIDED BY THE LENGTH OF SIDE B OR SINE 30 DEGREES
DIVIDED BY B MUST EQUAL, LET'S GO AHEAD
AND USE THE SAME RATIO OF SINE 18 DEGREES DIVIDED BY 7.
NOW IT'S THE SAME PROCESS, WE'LL CROSS MULTIPLY,
AND THEN SOLVE FOR B.
SO WE HAVE B x SINE 18 DEGREES MUST EQUAL 7 x THE SINE
OF 30 DEGREES.
SO NOW, WE'LL DIVIDE BY SINE 18 DEGREES AGAIN,
AND THIS QUOTIENT WILL GIVE US THE LENGTH OF SIDE B.
SO OUR NUMERATOR IS 7 SINE 30 DEGREES
DIVIDED BY SINE 18 DEGREES, SO THE LENGTH OF SIDE B
IS APPROXIMATELY 11.3 METERS.
AND NOW, WE HAVE THE LENGTH OF ALL OF THE SIDES
AND THE MEASURE OF ALL OF THE ANGLES,
SO WE HAVE SOLVED THIS TRIANGLE.