Measuring Lengths: Creative estimation of a tree height-1

Measuring Lengths involves measuring distance between two fixed points. length is a one dimension quantity. The SI unit for length is the meter (m).
Other units of length are indicated in the table below.

MEASUREMENT OF LENGTH
Length can be estimated or measured accurately using appropriate measuring instrument. The type of instrument to be used at any time depends on two factors:

• The size of the object to be measured
• The desired accuracy
  The methods used include;
  a) Approximation/ Estimation
  b) Accurate measuring using standard instruments

Measuring Lengths: Estimating height of a tree

This method involves comparing the object to be measured with length of another object that has a known length. For example, the height of a tall flag post can be compared with that of a wooden rod whose length is known.

Estimations can be done by comparing the sizes of objects directly or sometimes it is better to compare length of an object with that of a chosen basic length called a standard length.

consider a straight rod of length two meters. The rod can be used to estimate height of a tree nearby because the length of their shadows is proportional to their length height. So we can measure length of the shadow caste by the rod and the one caste by the tree. Note that it can be difficult to measure the actual height of the tree using measuring instruments, but by comparing it with that of a straight rod whose height is known, will give quite an accurate approximation of the tree height.

The following formula is be applied to applied to determine the height of a tree using a straight rod:

Suppose there is a tree whose shadow is measured with a measuring tape at 4.00 pm and its shadow is found to be 36.46m. Let us take the length of the shadow caste by our straight rod of 2m to be 6.42m. The height of the tree can then be calculated as:

hence

Height of the given tree is therefore approximately 11.7484 meters given in 4 decimal places.

Example Question

In estimating the height of a tree, the following measurements were recorded:
Height of the rod = 180cm.
Length of the shadow of the rod = 116cm
Length of the shadow of the tree = 420cm
Calculate the height of the tree.

Answer

Converting Kilometers to miles

1 kilometer (km) = 0.621371192 miles (mi).

To convert kilometers to miles, we multiply the number of kilometers by the conversion factor (0.621371192) to get the equivalent distance in miles. For example, if you have 10 kilometers and you want to convert it to miles, for example:

20 km × 0.621371192 miles/km = 12.42742384 miles

So, 20 kilometers is approximately equal to 12.42 miles.

Converting centimeter to Inches

The conversion factor between centimeters and inches can be found from the relationship:

1 centimeter (cm) = 0.393701 inches (in)

To convert centimeters to inches, you multiply the number of centimeters by the conversion factor (0.393701) to get the equivalent length in inches. For example, if you have 50 centimeters and you want to convert it to inches:

50 cm × 0.393701 in/cm ≈ 19.68505 inches

So, 50 centimeters is approximately equal to 19.68 inches.

Converting inches to feet

There are 12 inches in a foot. So, to convert inches to feet, you divide the number of inches by 12. For example, if you have 36 inches and you want to convert it to feet:

36 inches ÷ 12=3 feet

36 inches ÷ 12=3 feet

So, 36 inches is equal to 3 feet.

24 inches ÷ 12=2 feet

24 inches ÷ 12=2 feet

So, 24 inches is equal to 2 feet.

Questions for practice

Click to find examination questions about measuring of lengths

Related pages

• Important Physics personality
• Physical quantities
• Measuring with a ruler
• Physical Quantities
• Length
• Reading a meter rule
• Measuring with a meter rule
• Area
• Area of irregularly shaped surfaces
• Volume
• Volume of regularly shaped objects
• Measuring volume of liquids
• Volume of irregular solids
• Measuring Mass
• Density
• Densities of some substances
• Questions on Measurements
• Integrating quadratic polynomials