CPM Homework Help : PC Problem 1-114

Harold, the happy concrete guy, got a call on the phone about some concrete he has to pour for an odd shaped triangular patio. The only information he got was that the side lengths were $5$ , $6$ , and $8$ meters long.

Find the angles for Harold so he can stay happy.

Hint 1(a):

Draw and label a diagram.

More Help (a):

Since no angle measures are given, what formula should be used?

Substitute and Simplify (a):

$6^2=5^2+8^2-2(5)(8)\cos{A}$

$36=89-80\cos{A}$

$-53 = -80\cos{A}$

$\frac{53}{80}=\cos{A}$

Hint Answer (a):

Law of Cosines

$a² = b² + c² - 2bc\left(\text{cos }A\right)$

Triangle, A B C, labeled as follows: side, A B, 8 meters, side, B C, 6 meters, side, A C, ,5 meters.

Hint 2(a):

Use the Law of Sines to find another angle.

$\frac{a}{\text{Sin}A} = \frac{b}{\text{Sin}B} = \frac{c}{\text{Sin}C}$

Find the area of the patio that Harold will be forming.

Step 1(b):

Draw a segment from angle C ⊥ to side $AB$ .
Label the intersection point $E$ .

Step 2(b):

Using the sine function, calculate the height, $EC$ .

Step 3(b):

Determine the area of $ΔABC$ by calculating half of the base ( $8$ ) times the height ( $EC$ ).

Answer (b):

$14.98 \text{ sq. meters}$