document.write( "Question 1083096: Find trigonometric functions of angle α in a rightangled triangle with hypotenuse = 13cm and leg (catheti) = 12 cm \n" ); document.write( "

Algebra.Com's Answer #697103 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Without a picture with side lengths and angle $\"alpha\"$ labeled,
\n" ); document.write( "or some other way to figure out if angle $\"alpha\"$ is opposite or adjacent to the 12-cm leg,
\n" ); document.write( "I cannot give you the trigonometric functions of angle $\"alpha\"$ ,
\n" ); document.write( "but I can draw your triangle as triangle ABC, with right angle at A,
\n" ); document.write( "and give you the trigonometric functions of acute angles B and C.
\n" ); document.write( "You will have o figure out which one is $\"alpha\"$ .
\n" ); document.write( "

B is the angle adjacent to the 12-cm leg, C is opposite the 12-cm leg.
\n" ); document.write( "You need the length, $\"x\"$ , of leg AC.
\n" ); document.write( "For that you use the Pythagorean theorem.
\n" ); document.write( "Applied to this triangle, it says
\n" ); document.write( " $\"x%5E2%2B%2812cm%29%5E2=%2813cm%29%5E2\"$
\n" ); document.write( " $\"x%5E2%2B144cm%5E2=169cm%5E2\"$
\n" ); document.write( " $\"x%5E2=169cm%5E2-144cm%5E2\"$
\n" ); document.write( " $\"x%5E2=25cm%5E2\"$
\n" ); document.write( " $\"x=5cm\"$
\n" ); document.write( "With that length you can calculate values of all trigonometric functions for the acute angles.
\n" ); document.write( "Then you use the definitions for trigonometric ratios for a right triangle
\n" ); document.write( " $\"sin%28angle%29=%22opposite_leg%22%2Fhypotenuse\"$ , and $\"cos%28angle%29=%22adjacent_leg%22%2Fhypotenuse\"$ .
\n" ); document.write( "You may know tangent defined as
\n" ); document.write( " $\"tan%28angle%29=sin%28angle%29%2Fcos%28angle%29\"$ ,
\n" ); document.write( "or you may have learned it as
\n" ); document.write( " $\"tan%28angle%29=%22opposite_leg%22%2F%22adjacent_leg%22\"$ .
\n" ); document.write( "If you are expected to calculate cotangent, secant and cosecant, you would use
\n" ); document.write( " $\"cot%28angle%29=1%2Ftan%28angle%29\"$ , $\"sec%28angle%29=1%2Fcos%28angle%29\"$ and $\"csc%28angle%29=1%2Fsin%28angle%29\"$ .
\n" ); document.write( "As a tutor, I would prefer to see you figure it out from this point on,
\n" ); document.write( "but I will give you the answers because
\n" ); document.write( "you are not here to be persuaded to do the work,
\n" ); document.write( "and the website tells me that tutors \"MUST SHOW ALL WORK.\"
\n" ); document.write( "

\n" ); document.write( "

\n" );