What is the exact value of the bottom length (ie. x)?

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Please give the answer in the form a + b √c

1 Answer
Jim G.
Jan 21, 2018

#x=12+12sqrt3#

Explanation:

#"using the "color(blue)"trigonometric ratio"#

#•color(white)(x)tantheta="opposite"/"adjacent"#

#"let "x=x_1+x_2#

#"where "x_1" is the base of the right triangle on the left"#

#"and "x_2" is the base of the right triangle on the right"#

#"consider the left hand right triangle"#

#rArrtan45^@=12/x_1#

#rArrx_1=12/(tan45^@)=12/1=12#

#"consider the right hand right triangle"#

#rArrtan30^@=12/x_2#

#rArrx_2=12/(tan30^@)=12/(1/sqrt3)xxsqrt3/sqrt3=12sqrt3#

#rArrx=x_1+x_2=12+12sqrt3#

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