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.

Answer 1

I don’t have the diagram or any angle measure, so the problem is ambiguous. Tell me whether triangle POQ is a right triangle and which vertex is the right angle, or upload the picture. Meanwhile here are the common interpretations and the formula for PQ in each case:

- If PO and OQ are the two legs (right angle at O): PQ is the hypotenuse,
PQ = sqrt(x^2 + 5^2) = sqrt(x^2 + 25).

- If PO is the hypotenuse (PO = x) and OQ = 5 is a leg: the other leg PQ is
PQ = sqrt(x^2 − 5^2) = sqrt(x^2 − 25) (requires x > 5).

- If OQ = 5 is the hypotenuse and PO = x is a leg: the other leg PQ is
PQ = sqrt(5^2 − x^2) = sqrt(25 − x^2) (requires x < 5).

- If it’s not a right triangle, I need an angle (or another side) to use sine/cosine or the Law of Cosines.

Give me the diagram or tell me which case applies (or give the value of x or any angle), and I’ll compute PQ and round to the nearest tenth.