Question

A 4.2m flagpole casts a shadow of 8.3 m. Beth casts a shadow of 2.2 m. If Beth is h meters tall, solve for h to be correct to one decimal place.

Answer 1

To find Beth's height, we use the principle of similar triangles. We set up a proportion with the flagpole's height and shadow and solve for Beth's height to get approximately 1.1 meters.

Step-by-step explanation:

To solve for Beth's height in meters, we can use similar triangles. The flagpole and its shadow create a triangle, and so do Beth and her shadow. The ratios of corresponding sides of similar triangles are equal. Thus, the ratio of the flagpole's height to its shadow's length is equal to the ratio of Beth's height to her shadow's length.

Using this proportion, we have:

Flagpole height / Flagpole shadow = Beth's height / Beth's shadow

Substituting the known values:

4.2m / 8.3m = h / 2.2m

Now we solve for h:

h = (4.2m × 2.2m) / 8.3m

h ≈ 1.1m

So, Beth's height, rounded to one decimal place, is approximately 1.1 meters.