How do you solve for x in the given problem using right triangle trigonometry?

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Answer 1 · 2018-04-10T08:06:34

#color(blue)(x=(10tan(46)tan(34))/(tan(46)-tan(34)))#

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Using the tangent function:

Triangle ABC

#tan(34)=x/y=>x=ytan(34) \ \ \ \ [1]#

Triangle DBC

#tan(46)=x/(y-10)=>x=(y-10)tan(46)#

#:.#

#ytan(34)=(y-10)tan(46)#

#tan(34)/tan(46)=(y-10)/y#

#y=10/(1-tan(34)/tan(46))=(10tan(46))/(tan(46)-tan(34))#

Substituting in #[1]#

#:.#

#color(blue)(x=(10tan(46)tan(34))/(tan(46)-tan(34)))#