In ΔOPQ, o = 6.6 inches, p = 2.1 inches and q=6 inches. Find the measure of ∠O to the nearest 10th of a degree.

The measure of ∠O is 97.2° to the nearest tenth

Step-by-step explanation:

To solve this question, we will use the cosine rule

In Δ OPQ

Side o is opposite to ∠O

Side p is opposite to ∠P

Side q is opposite to ∠Q

By using the cosine rule

∵ o² = p² + q² - 2(p)(q)cos∠O

∵ o = 6.6 inches

∵ p = 2.1 inches

∵ q = 6 inches

→ Substitute them in the rule above

∴ (6.6)² = (2.1)² + (6)² - 2(2.1)(6)cos∠O

∴ 43.56 = 4.41 + 36 - 25.2cos∠O

→ Add the like terms in the right side

∴ 43.56 = 40.41 - 25.2cos∠O

→ Subtract 40.41 from both sides

∵ 3.15 = -25.2cos∠O

→ Divide both sides by -25.2 to find cos∠O

∴ -0.125 = cos∠O

→ Use your calculator to find ∠O

∵ m∠O =

∴ m∠O = 97.18075578

→ Round it to the nearest tenth ⇒ 2d.p.

∴ m∠O = 97.2°

h= 12 inches

step-by-step explanation: