Practical applications and Chapter II review

To find the height AH of a tree or building, stand at a point B at distance a from the base and measure the angle α to the top. From the right triangle ABH, AH = a·tgα. If the base cannot be approached, take points B and C in line with H, measure BC = a and the angles α (from B) and β (from C); by the law of sines in triangle ABC, AB = a·sinβ/sin(α − β), then AH = AB·sinα = a·sinα·sinβ/sin(α − β). For an inaccessible distance AB, choose a point C visible from A, measure AC = a, ∠A = α and ∠C = γ, and AB = a·sinγ/sin(α + γ). A protractor with a weighted string can serve as an angle meter. Do measurements with adults in a safe place; never measure beside a river or road.