A building is 100 m tall and the observation point is 80 m away. We find the angle of elevation using tan theta and smart estimation.
“Let’s carefully understand the problem first.” “A building is 100 meters tall.” Angle of elevation means the angle made with the ground while looking upward. “From a point 80 meters away from the base, we are looking at the top of the building.” “We are asked to find the angle of elevation.”
“Always imagine a right-angled triangle in heights and distances.” Explain verbally: Building = vertical side Distance on ground = horizontal side Line of sight = hypotenuse So: Height (opposite) = 100 m Distance (adjacent) = 80 m
“Now check which sides are involved.” “We know opposite side and adjacent side.” “So we will use tan theta.”
“Substitute the given values.”
“Now we don’t need exact calculation.” “We just need the closest angle from the options.” Recall: tan 45 ∘ = 1 tan45 ∘ =1 tan 60 ∘ ≈ 1.73 tan60 ∘ ≈1.73 “Since 1.25 lies between 1 and 1.73, the angle will be between 45° and 60°, and closer to 60°.”
“So the correct answer is 60 degrees.” “Remember this for exams.”
