Question

Find C. A. 7/2. B. 7/3. C. 9/2. D. 9. CB is 7. CA is 7. AB is c.

Answer 1

I’m not sure what “Find C.” means here — do you mean
- find the measure of angle C, or
- find the side AB (you labeled it c), or
- find some other quantity (altitude from C, median, inradius, circumradius, …)?

Given CB = CA = 7 and AB = c, the triangle is isosceles (equal sides meeting at C). Useful formulas:

- Law of cosines (gives angle C):
cos C = (CA^2 + CB^2 − AB^2) / (2·CA·CB) = (98 − c^2)/98,
so C = arccos((98 − c^2)/98).

- Altitude from C to AB (and also median/angle-bisector in this isosceles case):
h = sqrt(7^2 − (c/2)^2) = sqrt(49 − c^2/4).

- Area:
Δ = (1/2)·c·h = (c/4)·sqrt(196 − c^2).

If you meant “find angle C,” I can compute C for each answer choice for c:
- If c = 7/2: cos C = 0.875 → C ≈ 29.0°
- If c = 7/3: cos C ≈ 0.944 → C ≈ 19.9°
- If c = 9/2: cos C ≈ 0.7934 → C ≈ 37.7°
- If c = 9: cos C ≈ 0.17347 → C ≈ 80.0°

Tell me which quantity you want (angle C, side c, altitude, area, etc.) and I’ll finish the calculation or pick the correct choice.