How do I find T?

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1 Answer
Jim G.
Mar 19, 2018

#t=sqrt2#

Explanation:

#"since it is a right triangle use "color(blue)"trig. ratio"#

#"there is a choice of 2 approaches here"#

#•color(white)(x)tan30^@="opposite"/"adjacent"=t/sqrt6#

#•color(white)(x)tan60^@=sqrt6/t#

#"using "color(blue)"exact values"#

#•color(white)(x)tan30^@=1/sqrt3=sqrt3/3" and "tan60^@=sqrt3#

#tan30^@=t/sqrt6#

#rArrt=sqrt6xxtan30^@=sqrt6xxsqrt3/3#

#color(white)(xxxxxxxxxxxxxx)=sqrt18/3=(3sqrt2)/3=sqrt2#

#color(red)"OR"#

#tan60^@=sqrt6/t#

#rArrt=sqrt6/(tan60^@)=sqrt6/sqrt3=sqrt(6/3)=sqrt2#

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