**Definition of Indirect Measurement**

- Indirect measurement is a technique that uses proportions to find a measurement when direct measurement is not possible.

**Examples of Indirect Measurement **

- The length of a pole in a picture is given as 4 inches. The scale of the picture is given to be 1 inch : 13 inches. By setting up a proportion, the length
*n*of the actual pole can be found.

Solving the proportion, we get

**Solved Example on Indirect Measurement **

A boy stands on the top of a building and the total length of shadows of the building and the boy is (

x+a) ft and the length of the shadow of the boy alone isxft. If the height of the building isbft, then find the height of the boy. [Givenx= 8,a= 160,b= 80.]

Choices:

A. 4 ft

B. 3.5 ft

C. 3 ft

D. None of the above

Correct Answer: A

Solution:

Step 1:Lethbe the height of the boy.

Step 2:ΔACE ~ ΔBCD, because the measure of angle EAC = measure of angle DBC and the measure of angle C = measure of angle C.

Step 3:Corresponding sides of similar triangles are proportional.

Step 4:The proportion here is:

Step 5:160(h+ 80) = 168 × 80 [Write the cross products.]

Step 6:160h+ 12,800 = 13,440 [Multiply.]

Step 7:160h= 640 [Simplify.]

Step 8:h= 4 [Divide both sides by 160 and Simplify.]

Step 9:So, the height of the boy is 4 ft.

**Related Terms for Indirect Measurement**

- Proportion
- Measurement