Consider the triangle ABC given below; use trig ratios to answer this question. what is the length of the shorter leg of triangle ABC? what is the length of the hypotenuse of triangle ABC?

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what is the length of the shorter leg of triangle ABC?
what is the length of the hypotenuse of triangle ABC?

please, show your work, thank you.

1 Answer
Jim G.
Feb 10, 2018

#10sqrt3,20sqrt3#

Explanation:

#"consider the right triangle on the right"#

#"which has BC as the hypotenuse, that is the shorter"#
#"leg of triangle ABC"#

#rArrsin60^@=15/(BC)#

#rArrBCsin60^@=15#

#rArrBC=15/(sin60^@)=15/(sqrt3/2)=(15xx2)/sqrt3#

#color(white)(xxxxxxxxxxxxxxxxxx)=30/sqrt3xxsqrt3/sqrt3=10sqrt3#

#"consider "triangleABC" with hypotenuse AC"#

#sin30^@=(BC)/(AC)=(10sqrt3)/(AC)#

#rArrAC=(10sqrt3)/(sin30^@)=(10sqrt3)/(1/2)=20sqrt3#

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