A surveyor needs to find the height of a building. She stands 50 metres away from the base of the building and measures the angle of elevation to the top as 35^.

Here are the solutions to the problems: 10. A surveyor needs to find the height of a building. She stands 50 metres away from the base of the building and measures the angle of elevation to the top as 35^. a) Explain which trigonometric ratio (sine, cosine, or tangent) she should use and why. She should use the tangent ratio. This is because the tangent ratio relates the opposite side (the height of the building, which is unknown) to the adjacent side (the distance from the building, which is known) with respect to the given angle of elevation. b) Calculate the approximate height of the building. c) Show all your working and round your answer to the nearest metre. Step 1: Identify the knowns and unknowns in the right-angled triangle formed by the building, the ground, and the line of sight. • Angle of elevation () = 35^ • Adjacent side (distance from building) = 50 m • Opposite side (height of building, h) = unknown The tangent ratio relates the opposite and adjacent sides: = oppositeadjacent. Step 2: Substitute the values into the tangent ratio. 35^ = (h)/(50 m) Step 3: Solve for h. h = 50 m × 35^ Step 4: Calculate the value and round to the nearest metre. h ≈ 50 m × 0.7002075 h ≈ 35.010375 m Rounding to the nearest metre, the height of the building is 35 m Last free one today — make it count tomorrow, or type /upgrade for unlimited.