Question

Find the distance between a tower and a building of height 65 m and 34 m, respectively, such that the distance between their top is 29 m.

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Answer 1

Height of the tower (T) = 65 m

Height of the building (B) = 34 m

Distance between their tops = 29 m

We can use the concept of similar triangles to find the distance between the tower and the building. The heights of the tower and the building, along with the distance between their tops, form two similar right triangles.

Let's denote the distance between the tower and the building as "D."

Using the property of similar triangles, we can set up the following proportion:

(Top of building) / (Distance between tops) = (Top of tower) / (Distance between tops + D)

Simplifying the proportion:

(34 m) / (29 m) = (65 m) / (29 m + D)

Now, cross-multiply and solve for D:

34 * (29 m + D) = 65 * 29 m

986 m + 34D = 1885 m

34D = 1885 m - 986 m

34D = 899 m

D = 899 m / 34

D ≈ 26.44 m

Therefore, the distance between the tower and the building is approximately 26.44 meters.