Question

Jack looks at a clock tower from a distance and determines that the angle of elevation of the top of the tower is 40°. John, who is standing 20 meters from Jack as shown in the diagram, determines that the angle of elevation to the top of the tower is 60°. If Jack’s and John’s eyes are 1.5 meters from the ground, how far is John from the base of the tower? Round your answer to the nearest tenth.

Answer 1

In Triangle ACD\[\tan(40)=\frac{y}{20+x}\] Equation 1
In Triangle BCD\[\tan(60)=\frac{y}{x}\] Equation 2
From equation 2 we have,\[y=xtan(60)=\sqrt{3}x\]
We put this value in equation 1\[\tan(40)=\frac{\sqrt{3}x}{20+x}\]
From calculator, tan(40)=0.84\[0.84=\frac{\sqrt{3}x}{20+x}\]\[16.8+0.84x\approx 1.73x\]\[0.89x=16.8\]\[x=\frac{16.8}{0.89}=18.87\approx18.9\]