Question 121

Two boys are on opposite sides of a tower of 80 meters height. They measures the angles of elevation of the top of tower as $$45^\circ$$ and $$60^\circ$$ respectively. The distance between two boys(in meters) is

Solution

let the boys are standing in the triangle $$\triangleABC$$ here D is the point in between AB

so the height is CD = 80 m and $$\angleCAD$$ = 45 and $$\angleCBD$$ = 60

so we can say that

tan45 = CD\AD = 80\AD $$\Rightarrow$$ AD = 80

tan60 = CD\BD = 80\BD $$\Rightarrow$$ BD = 80\$$\sqrt{3}$$

so that the total ditance is AD + BD = 80 + 80\$$\sqrt{3}$$

$$\frac{80}{3}(3+\sqrt{3})$$ answer

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