Question

At a certain time of day 1.8m tall person standing next to the Washington monument cast a 0.7m shadow at the same time the Washington monument cast a 65.8m shadow how tall is Washington monument

Please help‍♀️

Answer 1

To find the height of the Washington Monument, we can use the concept of similar triangles and set up a proportion based on the given measurements. By cross-multiplying, we deduce that the Washington Monument is approximately 169.2 meters tall.

Step-by-step explanation:

The problem presented is a classic example of using similar triangles to determine the height of the Washington Monument. Since the 1.8m tall person and the Washington Monument cast shadows at the same time, we can assume that the sunlight angles are the same for both, creating similar triangles. To find the height of the monument, we can set up a proportion:

Person's height / Person's shadow = Monument's height / Monument's shadow

1.8m / 0.7m = Monument's height / 65.8m

By cross-multiplying, we find:

(1.8m * 65.8m) / 0.7m = Monument's height

118.44m / 0.7m = Monument's height

Therefore, the height of the Washington Monument is approximately 169.2 meters.

Answer 2

169 m

Step-by-step explanation:

See the image below.

Line AB represents the monument and line BC its shadow

Line DB represents the man and Line BE it shadow.

The Sun’s rays are parallel, so AC||DE.

Then ∆ABC ~ ∆DBE

AB:BC::DB:BE

x/65.8 = 1.8/0.7 Multiply both sides by 65.8

x = 65.6 × 1.8/0.7

x = 65.6 × 2.571

x = 169 m

The height of the Washington monument is 169 m.