Question

Find the length of the third side. If necessary, round to the nearest tenth.
26
24

Answer 1

I’m missing the triangle context — do 26 and 24 represent two legs of a right triangle, one leg and the hypotenuse, two sides with a known included angle, or just two sides (asking for the possible range of the third side)?

Here are the common interpretations and results:

- If 26 and 24 are the legs of a right triangle, the hypotenuse = sqrt(26^2 + 24^2) = sqrt(1252) ≈ 35.4.

- If 26 is the hypotenuse and 24 is a leg, the other leg = sqrt(26^2 − 24^2) = sqrt(100) = 10.

- If 26 and 24 are two sides with an unknown included angle θ, the third side (by the Law of Cosines) is
c = sqrt(26^2 + 24^2 − 2·26·24·cos θ),
so you need θ to get a numeric value.

- If you only know two side lengths (26 and 24) and nothing else, the triangle inequality says the third side must satisfy 2 < x < 50.

Tell me which case applies (or give the angle), and I’ll give the exact numeric answer.