Tuesday, August 02, 2016

Daily Regents: Similar Triangles are Proportional (August 2015)

Even though the title says "Daily", I won't be doing them daily any more, until the exams get closer. But they will be frequent.

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.

Use the surveyor’s information to determine and state the distance from point B to point C, to the nearest yard

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.

No comments: