Question

Use trig to find a side. Solve for x. Round to the nearest tenth, if necessary. PO number is x OQ number is 5. What is the number for PQ. The angle for this number is 42.

Answer 1

I need one quick clarification: is triangle POQ a right triangle with the right angle at P (so PO is the hypotenuse)? If yes, then angle O = 42°, OQ (adjacent to angle O) = 5, and PO = x. If that matches your diagram, proceed as below.

Using cosine for angle O:
cos 42° = adjacent/hypotenuse = OQ/PO = 5/x
=> x = 5 / cos 42° ≈ 5 / 0.7431448 ≈ 6.7 (to the nearest tenth).

Then PQ is the side opposite angle O. Use sine (or tangent):
PQ = x·sin 42° = (5 / cos 42°)·sin 42° = 5·tan 42° ≈ 5·0.900404 = 4.5 (to the nearest tenth).

So x ≈ 6.7 and PQ ≈ 4.5. If the triangle is arranged differently, please upload or describe the diagram and I’ll adjust.