Exercise 29 Page 504

Let's start by determining what type of triangle is given.

Determining the Part of the Triangle

We can see that the given right triangle has a 30 ° angle, and therefore, this is a 30 °-60 °-90 ° triangle. In a 30 °-60 °-90 ° triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is sqrt(3) times the length of the shorter leg. Let's look at the given triangle.

The shorter leg, s, is always opposite the 30 ° angle. The conveyor belt is opposite the 90 ° angle, so it represents the hypotenuse.

Finding Time

We are given the speed of the conveyor belt. Let's recall the formula for speed. Speed=Distance/Time To find the time it takes for a bale of hay to go from the ground to the barn loft, we need to find this distance. The distance of the conveyor belt is equal to the length of the hypotenuse. To find the hypotenuse, we will use the fact that the length of the shorter leg s= 12 feet. Hypotenuse=2 s ⇕ Hypotenuse=2( 12)=24 The length of the conveyor belt is equal to 24 feet. Let's start by finding the time in minutes it takes the hay to move up the conveyor belt. We will substitute the given speed of 100 feet per minute and the distance of 24 feet into the formula for speed and solve for the time.

Speed=Distance/Time

SubstituteII

Speed= 100 ft/min, Distance= 24 ft

100 ft/min=24 ft/Time

MultEqn

LHS * Time=RHS* Time

100 ft/min * (Time) = 24 ft

DivEqn

.LHS /100 ft/min.=.RHS /100 ft/min.

Time= 24 ft/100 ft/min

CancelCommonFac

Cancel out common factors

Time= 24 ft/100 ft/min

DivByFracSL

.a /b/c.=a* c/b

Time= 24 min/100

SimpQuot

Simplify quotient

Time= 0.24 min

It takes the bale of hay 0.24 minutes to move from the ground to the barn loft.

Minutes to Seconds

Finally, we need to convert this time in minutes to seconds. To do this, we will use the following conversion factor. 60sec/1min Multiplying 0.24min by this conversion factor will convert it to seconds.

0.24min*60sec/1min

Multiply

Multiply

0.24 min * 60sec/1min

CrossCommonFac

Cross out common factors

0.24 min * 60sec/1min

SimpQuot

Simplify quotient

0.24* 60sec/1

DivByOne

a/1=a

0.24* 60sec

UseCalc

Use a calculator

14.4sec

It takes 14.4 seconds for a bale of hay to go from the ground to the barn loft.