- IN THESE EXAMPLES WE WANT TO USE A TRIG EQUATION
TO DETERMINE THE LENGTH OF A SIDE OF A RIGHT TRIANGLE.
SO LOOKING AT OUR DIAGRAM HERE,
IF WE USE THE ANGLE THAT MEASURES 34 DEGREES,
THIS SIDE OF THE TRIANGLE WOULD BE THE OPPOSITE SIDE.
AND THIS SIDE HERE IS OPPOSITE THE RIGHT ANGLE,
SO THIS WOULD BE THE HYPOTENUSE.
SO THE TRIG FUNCTION THAT INVOLVES THE OPPOSITE
AND THE HYPOTENUSE WOULD BE THE SIGN FUNCTION.
SO OUR TRIG EQUATION IS GOING TO BE THE SIGN OF 34 DEGREES
WOULD BE EQUAL TO THE RATIO OF X TO 27 INCHES.
AND WE'LL GO AHEAD AND LEAVE OFF THE INCHES FOR RIGHT NOW.
AND I ALWAYS FIND IT HELPFUL TO WRITE THIS AS A PROPORTION,
SO I'M GOING TO GO AHEAD
AND PUT THE SIGN OF 34 DEGREES OVER 1.
AND NOW THAT WE HAVE A PROPORTION,
WE CAN CROSS MULTIPLY, AND THEN SOLVE FOR X.
SO 1 x X WOULD BE X MUST = 27 x SIGN 34 DEGREES.
AND NOW WE'LL GO AHEAD AND GO TO OUR CALCULATOR
TO DETERMINE THIS PRODUCT.
FIRST THING WE NEED TO DO,
IS MAKE SURE THAT WE'RE IN DEGREE MODE.
SO WE'LL PRESS THE MODE KEY, ARROW DOWN TO THE THIRD ROW,
RIGHT OVER ONCE TO DEGREE, PRESS ENTER.
AND NOW WE'LL GO BACK TO THE HOME SCREEN, SECOND, QUIT.
WE'LL TYPE IN 27 x SIGN 34 DEGREES.
AND X IS APPROXIMATELY 15.1 INCHES.
HERE'S OUR SECOND EXAMPLE.
AGAIN, IF WE USE THIS ANGLE HERE THAT MEASURES 56 DEGREES,
THIS WOULD BE THE OPPOSITE SIDE,
THIS WOULD BE THE HYPOTENUSE,
AND THIS WOULD BE THE ADJACENT SIDE.
SO FOR THIS PROBLEM WE WANT TO USE THE TRIG FUNCTION
THAT INVOLVES THE ADJACENT SIDE AND THE HYPOTENUSE,
AND THAT WOULD BE THE COSIGN FUNCTION.
SO WE'RE GOING TO HAVE THE COSIGN OF 56 DEGREES
WOULD BE EQUAL TO 16 TO X.
NOW, BECAUSE THIS IS THE RIGHT TRIANGLE,
WE COULD DETERMINE THE MEASURE OF THIS ANGLE HERE
AND THEN USE A DIFFERENT TRIG FUNCTION,
BUT I'M SETTING THESE UP USING JUST THE GIVEN INFORMATION.
LET'S GO AHEAD AND MAKE THIS A PROPORTION,
AND NOW WE CAN CROSS MULTIPLY X x COSIGN 56 DEGREES
MUST EQUAL 16 x 1, WHICH IS 16.
NOW, FOR HERE TO SOLVE FOR X, WE HAVE TO DIVIDE.
WE'LL DIVIDE BOTH SIDES BY COSIGN 56 DEGREES,
SO WE'D HAVE X IS APPROXIMATELY EQUAL
TO THIS QUOTIENT.
LET'S GO BACK TO THE CALCULATOR
AND WE'LL HAVE 16 DIVIDED BY COSIGN 56 DEGREES.
SO FOR THIS PROBLEM X IS APPROXIMATELY 28.6
AND THIS IS METERS.
LET'S GO AND TAKE A LOOK AT ONE MORE EXAMPLE.
AGAIN, WE'RE GIVEN THIS ANGLE THAT MEASURES 71 DEGREES,
SO THIS SIDE HERE WOULD BE THE OPPOSITE SIDE.
THIS SIDE OPPOSITE THE RIGHT ANGLE IS THE HYPOTENUSE,
SO THIS SIDE HERE WOULD BE THE ADJACENT SIDE.
SO WE WANT THE TRIG FUNCTION
THAT INVOLVES THE OPPOSITE SIDE AND THE ADJACENT SIDE.
SO NOW WE'LL USE THE TANGENT FUNCTION.
THE TANGENT OF 71 DEGREES IS EQUAL TO THE RATIO
OF THE LENGTH OF THE OPPOSITE SIDE
TO THE LENGTH OF THE ADJACENT SIDE, SO X TO 5.
WRITE IT AS A PROPORTION AND NOW WE'LL CROSS MULTIPLY
X x 1 WOULD BE X AND 5 x TANGENT 71 DEGREES.
NOW WE'LL GO TO THE CALCULATOR,
5 TANGENT 71 DEGREES,
AND SO X IS APPROXIMATELY 14.5.
AND THIS IS CENTIMETERS.
I HOPE YOU FOUND THESE EXAMPLES HELPFUL.