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Chelsea is sitting 88 feet from the foot of a tree. From where she is sitting, the angle of elevation of her line of sight to the top of the tree is 36∘36^{\circ}. If her line of sight starts 1.51.5 feet above ground, how tall is the tree, to the nearest foot?\newline(1) 88\newline(2) 77\newline(3) 66\newline(4) 44

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Q. Chelsea is sitting 88 feet from the foot of a tree. From where she is sitting, the angle of elevation of her line of sight to the top of the tree is 36∘36^{\circ}. If her line of sight starts 1.51.5 feet above ground, how tall is the tree, to the nearest foot?\newline(1) 88\newline(2) 77\newline(3) 66\newline(4) 44
  1. Identify Relationship: : Identify the relationship between the angle of elevation, the distance from Chelsea to the tree, and the height of the tree above Chelsea's line of sight.\newlineWe can use the tangent of the angle of elevation to relate the height of the tree above Chelsea's line of sight to the distance from Chelsea to the tree. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
  2. Calculate Height: : Calculate the height of the tree above Chelsea's line of sight using the tangent function.\newlineThe tangent of 3636 degrees is equal to the height of the tree above Chelsea's line of sight (let's call this height 'hh') divided by the distance from Chelsea to the tree, which is 88 feet.\newlinean(36∘)=h8 an(36^\circ) = \frac{h}{8}
  3. Solve for 'h': : Solve for 'h' by multiplying both sides of the equation by 88.\newlineh=8×tan⁡(36∘)h = 8 \times \tan(36^\circ)\newlineUsing a calculator, we find that tan⁡(36∘)\tan(36^\circ) is approximately 0.72650.7265.\newlineh=8×0.7265h = 8 \times 0.7265\newlineh≈5.812h \approx 5.812 feet
  4. Add Heights: : Add Chelsea's line of sight height above the ground to the height of the tree above her line of sight.\newlineThe total height of the tree is the height above Chelsea's line of sight plus the 1.51.5 feet from the ground to her line of sight.\newlineTotal height of the tree = h+1.5h + 1.5 feet\newlineTotal height of the tree ≈5.812+1.5\approx 5.812 + 1.5 feet\newlineTotal height of the tree ≈7.312\approx 7.312 feet
  5. Round Total Height: : Round the total height of the tree to the nearest foot.\newlineThe total height of the tree, rounded to the nearest foot, is 77 feet.

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