Question

To indirectly measure the distance across a lake, Ethan makes use of a couple

landmarks at points B and C. He measures AE, EC, and DE as marked. Find the
distance across the lake (BC), rounding your answer to the nearest hundredth of a
meter.

Answer 1

To find the distance across the lake, use the method of similar triangles and set up a proportion. Solve for the length of BC using the given side lengths of AE, EC, and DE.

Step-by-step explanation:

To indirectly measure the distance across the lake, we can use the method of similar triangles. Let's consider the triangle AEC and the triangle BDC. Since the angles AEC and BDC are both right angles, we can conclude that these two triangles are similar. This means that the ratios of their corresponding side lengths are equal.

Given that AE = 100 m, EC = 80 m, and DE = 60 m, we can set up a proportion to find the length of BC:

AE/EC = DE/BC

Simplifying the proportion, we have:

100/80 = 60/BC

Cross multiplying, we get:

100 * BC = 80 * 60

Solving for BC, we have:

• BC = (80 * 60) / 100
• BC = 48 m

Therefore, the distance across the lake, BC, is approximately 48 meters.