*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:

Post a Comment