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A tree standing vertically on level ground casts a 140 foot long shadow. The angle of elevation from the end of the shadow to the top of the tree is 19.8°. Find the height of the tree to the nearest foot

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Solving using trigonometry, the height of the tree to the nearest foot is 50 feets

USING SOHCAHTOA :

  • Opposite = height, h
  • Adjacent, = 140 feets
  • Angle, θ = 19.8°

Tanθ = opposite / Adjacent

Tan(19.8) = h / 140

Cross multiply :

h = 140 × tan(19.8)

h = 50.403 feets

Height, h = 50 feets (nearest foot)

Therefore, the height of the tree is 50 feets

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