Question

The height of a horse is usually measured in hands. One hand is exactly \(1 / 3 \mathrm{ft}\) (a) How tall (in feet) is a horse of 19.2 hands? (b) How tall (in meters) is a horse of 17.8 hands? (c) A horse of 20.5 hands is to be transported in a trailer. The roof of the trailer needs to provide \(3.0 \mathrm{ft}\) of vertical clearance. What is the minimum height of the trailer in feet?

Short answer

Answer: A 17.8-hand tall horse is approximately 1.8192 meters tall.

Step-by-step solution

Convert hands to feet

To convert hands to feet, we will use the conversion factor given in the exercise: 1 hand = 1/3 ft. For part (a), we need to convert 19.2 hands to feet. To do this, we'll multiply the number of hands by the conversion factor: 19.2 hands × (1/3 ft/hand) = 19.2/3 ft = 6.4 ft

Convert hands to meters

Before we can convert 17.8 hands to meters for part (b), we must first convert it to feet, and then to meters. 1 ft = 0.3048 meters, so we will use that conversion factor as well. 17.8 hands × (1/3 ft/hand) × (0.3048 m/ft) = 17.8/3 × 0.3048 m ≈ 1.8192 m

Calculate the minimum height of the trailer

For part (c), we need to determine the height of a trailer that will accommodate a horse of 20.5 hands with an additional 3.0 ft of vertical clearance. First, we'll convert 20.5 hands to feet: 20.5 hands × (1/3 ft/hand) = 20.5/3 ft ≈ 6.833 ft Next, add the required 3.0 ft of vertical clearance to the horse's height: 6.833 ft + 3.0 ft = 9.833 ft So the minimum height of the trailer must be 9.833 feet.

Key concepts

Conversion of Hands to Feet

Understanding how to convert 'hands' to 'feet' is key in various scenarios, particularly when dealing with the measurement of horses, as is standard practice in the equine world. One hand is equal to exactly one-third of a foot. To put this into perspective, picture the width of an adult's hand - it is approximately four inches wide, which is the historical basis for the unit. This conversion might seem unconventional, but it is quite simple once you grasp the concept.

Let's illustrate the conversion with an example. If a horse stands 19.2 hands, the calculation to convert this measurement to feet is straightforward. You multiply the number of hands (19.2) by the conversion factor (1/3 ft per hand), which gives us:
$$19.2 \, \text{hands} \times \left(\frac{1}{3} \, \text{ft/hand}\right) = \frac{19.2}{3} \, \text{ft}$$
And upon doing the math, we find that 19.2 hands is equal to 6.4 feet. It's all about multiplying by that conversion factor to switch from the unit of 'hands' to the more commonly used 'feet'.

Conversion of Feet to Meters

Once we're comfortable converting 'hands' to 'feet', the next step often required is converting 'feet' to 'meters', especially when we're dealing in international or scientific contexts where the metric system is standard. There's a globally accepted conversion factor for this: 1 foot is equivalent to 0.3048 meters.

Let's apply this to an example. If you already converted a horse's height from hands to feet and found it to be 6.4 feet, to get the height in meters, do the following calculation:
$$6.4 \, \text{ft} \times 0.3048 \, \text{m/ft} = 1.95072 \, \text{m}$$
For a horse that measures 17.8 hands, first convert to feet and then to meters:
$$17.8 \, \text{hands} \times \left(\frac{1}{3} \, \text{ft/hand}\right) \times 0.3048 \, \text{m/ft} = 1.8192 \, \text{m}$$
This two-step process is essential for converting measurements from the imperial to the metric system, which is widely used around the world.

Calculating Clearance Height

Calculating clearance height is a practical application of unit conversion that can be crucial in situations like transporting animals or goods. Clearance height refers to the minimum vertical space required above an object — in this case, a horse — to ensure it fits comfortably within a space, such as a trailer.

For our example, a horse standing 20.5 hands tall needs to be transported, and the trailer must provide an additional 3.0 feet of vertical clearance. After converting the horse's height to feet, we must add the vertical clearance to this measurement:
$$\text{Horse's height in feet (20.5 hands)} + \text{Vertical clearance (3.0 feet)} = \text{Minimum trailer height in feet}$$
Thus, if the horse is 6.833 feet tall after conversion, the minimum trailer height should be:
$$6.833 \, \text{ft} + 3.0 \, \text{ft} = 9.833 \, \text{ft}$$
This calculation ensures that the trailer will be tall enough to both accommodate the horse and allow for enough space overhead to avoid any injury or discomfort during transportation.