### Home > PC > Chapter 1 > Lesson 1.3.2 > Problem1-114

1-114.
1. 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. Homework Help ✎

1. Find the angles for Harold so he can stay happy.

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

Draw and label a diagram.

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

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

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

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

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

Law of Cosines
a² = b² + c² - 2bc(cos A)

Use the Law of Sines to find another angle.

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

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

Using the sine function, calculate the height, EC.

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

14.98 sq. meters