Question

To indirectly measure the distance across a lake, Brayden makes use of a couple landmarks at points C and D. He measures BF, FD, and EF as marked. Find the distance across the lake (CD)

Answer 1

The distance across the lake (CD) is equal to EF.

Step-by-step explanation:

Brayden used the measurements BF, FD, and EF to indirectly determine the distance across the lake (CD). According to the information provided, the length EF represents the distance from point C to point D. This is because BF is a common side shared by triangles BCF and BDE, and FD is the difference in the lengths of BC and BE. By using the triangle similarity theorem, we can conclude that triangles BCF and BDE are similar.

Since corresponding sides of similar triangles are proportional, BF/BC = FD/BE. Given that BF and FD are measured, and BE is the sum of BF and EF, Brayden can use this information to calculate EF. Once EF is determined, it represents the distance from point C to point D across the lake. This indirect measurement technique relies on the principles of triangle similarity and proportionality, allowing Brayden to find the distance CD without directly measuring it.