a Evaluate the perimeter of the pennant using the definition of cosine.
B
b Start with converting inches to yards.
A
a ≈ 494.3 inches
B
b $8.95
Practice makes perfect
a We are asked to determine the total length of seam binding that Hana needs to finish the edges of the pennants. This means that we should find the perimeter of one pennant and then multiply it by the number of girls.
As we have two right triangles, we can use trigonometric ratios to evaluate the length of the missing sides. Let's recall the definition of the cosine of an angle.
If△ ABCis a right triangle with acute∠A,
then the cosine of∠Ais the ratio of the length of the leg adjacent∠A to the length of the hypotenuse.
Let's look at our picture and label the missing sides lengths x.
Now we can write an equation for cos 70^(∘). The length of the leg adjacent to 70^(∘) is 3.5, and the hypotenuse has a length of x.
cos 70^(∘)=3.5/x
Let's solve above equation.
The length of the missing side is approximately 10.23 inches.
Now we can evaluate the approximate perimeter of the pennant.
7in.+10.23in.+10.23in.=27.46
The perimeter of one pennant is approximately 27.46 inches. To calculate the total length of seam binding, we will multiply this perimeter by the number of girls, which is 18.
27.46*18= 494.3
Hana needs approximately 494.3 inches of seam binding to make the pennants for her basketball team.
b We are given that seam binding is sold in 3-yard packages at a cost of $1.79 and asked to evaluate the total cost of seam binding. Since we evaluated the length of seam binding in inches the first step will be to convert inches to yards.
494.3in.=494.3*1yd/36in.≈ 13.73ydNext, we will divide this total length by 3 to get the number of packages Hana needs. Notice that in this case we will round the result to the nearest integer that is not less than the exact number.
13.73/3=4.576...≈ 5
Hana needs to buy 5 packages of seam binding. Finally, we will multiply the number of packages by the unit price, $1.79.
5* 1.79=8.95
It will cost $8.95.
