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Chapter 1: Problem 35

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

Expert verified
Question: Convert the following horse heights and find the minimum height of the trailer: (a) 19.2 hands to feet (b) 17.8 hands to meters (c) Minimum height of the trailer considering a 20.5 hands horse height and a 3.0 feet required clearance Answer: (a) 6.4 feet (b) 1.808 meters (c) 9.8333 feet

Step by step solution

01

Part (a): Convert 19.2 hands to feet

To convert the height of the horse in hands to feet, we need to multiply the number of hands (19.2) by the conversion factor (1/3 ft per hand): \(19.2 \text{ hands} \times \frac{1}{3} \text{ ft/hand} = 6.4 \text{ ft}\) So, the horse is 6.4 feet tall.
02

Part (b): Convert 17.8 hands to meters

First, we need to convert the horse height from hands to feet: \(17.8 \text{ hands} \times \frac{1}{3} \text{ ft/hand} = 5.9333 \text{ ft}\) Then, we will convert the height in feet to meters using the conversion factor (1 ft = 0.3048 meters): \(5.9333 \text{ ft} \times 0.3048 \text{ m/ft} = 1.808 \text{ m}\) So, the horse is approximately 1.808 meters tall.
03

Part (c): Calculate the minimum height of the trailer in feet

First, we need to determine the height of the horse in feet: \(20.5 \text{ hands} \times \frac{1}{3} \text{ ft/hand} = 6.8333 \text{ ft}\) Next, we need to add the required clearance of 3.0 feet to the horse's height: \(6.8333 \text{ ft} + 3.0 \text{ ft} = 9.8333 \text{ ft}\) So, the minimum height of the trailer should be approximately 9.8333 feet.

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