WORD PROBLEMS ON INDIRECT MEASUREMENT SIMILAR TRIANGLES

If two triangles are equiangular, then those two triangles are similar. Then, ratio of the corresponding sides will be equal.

Problem 1 :

Use similar triangles to find the height of the building.

Solution : 

Height of the smaller triangle = 6 ft

Base of the smaller triangle = 13 ft

Height of the larger triangle = h

Base of the larger triangle = 39 ft

Use the proportion,

So, height of the larger triangle is 18 ft.

Problem 2 :

Use similar triangles to find the height of the tree.

Solution:

Given, height of the smaller triangle = 3 m

Base of the smaller triangle = 4 m

Height of the larger triangle = h

Base of the larger triangle = 36 m

Use the proportion,

So, height of the larger tree is 27 m.

Problem 3 :

A lamppost casts a shadow that is 15 yards long. A 3 foot tall mailbox casts a shadow that is 5 yards long. How tall is the lamppost?

Solution:

Use the proportion,

So, the lamppost is 9 yards.

Problem 4 :

An 8 foot tall statue stands in the park and casts a shadow that is 16 feet long. A dog stands next to it and is 3 feet tall. How long is the dog's shadow?

Solution:

Use the proportion,

So, length of the dog's shadow is 6 feet.

Problem 5 :

A building casts a shadow that is 420 meters long. At the same time, a person who is 2 meters tall casts a shadow that is 24 meters long. How tall is the building?

Solution:

Use the proportion,

So, height of the building is 35 meters.

Problem 6 :

On a sunny day around noon, a tree casts a shadow that is 12 feet long. At the same time, a person who is 6 feet tall standing beside the tree casts a shadow that is 2 feet long. How tall is the tree?

Solution:

Use the proportion,

So, height of the tree is 36 feet.