Geometry, August 2015, Question 27
27. To find the distance across a pond from point B to point C, a surveyor drew the diagram below. The measurements he made are indicated on his diagram.
There are two right triangles. Right angles are congruent.
Both triangles contain angle A. Reflexive Property says angle A is congruent to itself.
Therefore, triangle ABC ~ ADE
If the triangles are similar, then their corresponding sides are proportional.
AE = 230, AC = 230 + 85 = 315. DE = 120. BC corresponds to DE.
Set up a proportion: AE / DE = AC / BC
230/120 = (230 + 85) / x
230 x = (120)(315)
230 x = 37800
x = 164.3478...
x = 164 yards
The distance from point B to point C is 164 yards.