What is the exact value of the bottom length (ie. x)?
Please give the answer in the form a + b √c
Please give the answer in the form a + b √c
1 Answer
Jan 21, 2018
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#