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- WELCOME TO EXAMPLES OF USING A TRIG EQUATION
TO DETERMINE THE MEASURE OF AN ANGLE IN A RIGHT TRIANGLE.
SO IN THIS DIAGRAM HERE
WE WANT TO DETERMINE THE MEASURE OF ANGLE THETA.
LET'S START BY IDENTIFYING WHAT INFORMATION WE HAVE.
IF THIS IS ANGLE THETA,
THIS SIDE HERE WOULD BE THE OPPOSITE SIDE,
AND THIS SIDE OPPOSITE THE RIGHT ANGLE WOULD HYPOTENUSE.
SO THIS TELLS US THAT WE WILL HAVE TO USE THE SIN FUNCTION
SINCE WE KNOW THE LENGTH OF THE OPPOSITE SIDE
AND THE LENGTH OF THE HYPOTENUSE.
SO SIN THETA WOULD HAVE TO BE EQUAL TO 10/27.
SO NOW WE JUST NEED TO SOLVE THIS EQUATION FOR THETA.
WE CAN DO THAT BY TAKING INVERSE SIN
OF BOTH SIDES OF THE EQUATION.
REMEMBER, WE COULD ALSO HAVE WRITTEN ARC SIN.
WELL IF AN INVERSE SIN OF SIN THETA,
THESE ARE INVERSES OF ONE ANOTHER
AND THEY UNDO EACH OTHER.
SO WE'RE LEFT WITH THETA ON THE LEFT SIDE OF THE EQUATION.
AND THEN WE CAN USE OUR CALCULATOR TO DETERMINE
INVERSE SIN 10/27.
REMEMBER, THIS IS GOING TO RETURN THE ANGLE
THAT HAS A SIN FUNCTION VALUE OF 10/27.
WE DO HAVE TO DECIDE IF WE WANT THETA IN DEGREES OR RADIANTS.
IF I PRESS THE MODE KEY NOTICE HOW I AM IN DEGREE MODE.
IF WE NEED THETA IN RADIANTS, WE WOULD HIGHLIGHT RADIANTS.
NOW WE'LL PRESS SECOND SIN.
THAT GIVES US INVERSE SIN, AND THEN 10 DIVIDED BY 27.
SO THETA IS APPROXIMATELY 21.7 DEGREES.
OF COURSE, IF WE NEEDED RADIANTS,
WE COULD CHANGE THE MODE OR DO THE CONVERSION.
BY MULTIPLYING BY PI DIVIDED BY 180 DEGREES.
LET'S TAKE A LOOK AT ANOTHER EXAMPLE.
IF THIS IS OUR ANGLE THETA,
THIS SIDE HERE WOULD BE THE OPPOSITE SIDE.
THE SIDE OPPOSITE THE RIGHT ANGLE WOULD BE THE HYPOTENUSE.
AND THIS SIDE HERE WOULD BE THE ADJACENT SIDE TO ANGLE THETA.
SO HERE WE'LL WRITE A TRICK EQUATION THAT INVOLVES
THE ADJACENT SIDE AND THE HYPOTENUSE,
THAT'S GOING TO BE THE COSINE FUNCTION.
SO COSINE THETA MUST EQUAL THE RATIO OF 35 TO 42.
AND NOW WE'LL TAKE INVERSE COSINE OF BOTH SIDES
OF THE EQUATION.
INVERSE COSINE OF COSINE THETA WILL GIVE US THETA.
AND NOW WE'LL GO BACK TO THE CALCULATOR.
PRESS SECOND COSINE 35 DIVIDED BY 42.
HERE THETA IS APPROXIMATELY 33.6 DEGREES.
LET'S GO AHEAD AND TAKE A LOOK AT ONE MORE EXAMPLE.
IF THIS IS THETA, THEN THE SIDE OF LENGTH FIVE CENTIMETERS
WOULD BE THE OPPOSITE SIDE.
THE SIDE OPPOSITE THE RIGHT ANGLE IS THE HYPOTENUSE.
AND THIS WOULD BE THE ADJACENT SIDE.
SO NOW I'LL NEED A TRIG EQUATION
THAT INVOLVES THE OPPOSITE SIDE AND THE ADJACENT SIDE,
AND THAT'S GOING TO BE THE TANGENT FUNCTION.
TANGENT THETA WOULD EQUAL FIVE DIVIDED BY 25.
AND NOW WE WILL TAKE THE INVERSE TANGENT OF BOTH SIDES
OF THE EQUATION.
INVERSE TANGENT OF TANGENT THETA WILL GIVE US THETA.
THEN WE'LL GO BACK TO OUR CALCULATOR.
INVERSE TANGENT WOULD BE SECOND TANGENT FIVE DIVIDED BY 25.
SO THETA IS APPROXIMATELY 11.3 DEGREES.
I HOPE YOU FOUND THIS HELPFUL.