Question

In △ OPQ, p=7.2cm, ∠ P=36° and ∠ Q=38°. Find the length of q, to the nearest 10th of a centimeter.

Answer 1

The length of side q in △ OPQ, given p = 7.2 cm,
`\angle P` = 36°, and

`\( \angle Q` = 38° , is approximately 7.60 cm.

To find the length of side q in △OPQ, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Let q be the length of side q. Using the Law of Sines:

`\[(p)/(\sin P) = (q)/(\sin Q)\]`

Substitute the given values:

`\[(7.2)/(\sin 36°) = (q)/(\sin 38°)\]`

Now, solve for q:

`\[q = (7.2 \cdot \sin 38°)/(\sin 36°)\]`

Using a calculator:

`\[q \approx (7.2 \cdot 0.6209)/(0.5878) \approx 7.60 \, \text{cm}\]`

Therefore, the length of side q is approximately 7.60 cm (rounded to the nearest tenth of a centimeter).