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

1 Answer
Apr 10, 2018

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

Explanation:

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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