How do you find the height, h of a mountain using the info given in figure 5.2.9?

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See http://www.chegg.com/homework-help/find-height-h-mountain-using-information-given-figure-529fig-chapter-5.2-problem-6e-solution-9781449649128-exc for the figure.

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Answer 1 · 2018-04-10T15:10:59

#tan(28)/(1-tan(28))# km# ~~1.135# km

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Using the tangent function.

#tan(theta)="opposite"/"adjacent"#

Triangle ABC

#tan(28)=h/y=>h=ytan(28) \ \ \ \ \[1]#

Triangle ADC

#tan(45)=h/(y-1)=h=(y-1)tan(45)#

This means:

#ytan(28)=(y-1)tan(45)#

#(y-1)/y=tan(28)/tan(45)#

#y=1/(1-tan(28)/tan(45))#

Substituting this in #[1]#

#h=tan(28)/(1-tan(28)/tan(45))=(tan(45)tan(28))/(tan(45)-tan(28))#

#tan(45)=1#

#h=tan(28)/(1-tan(28))#

Height of mountain is:

#tan(28)/(1-tan(28))# km# ~~1.135# km