Asked by joy
Question content area top
Part 1
Find the measure of side b.
40
o
c = 310 in.
b
All Answers 1
Answered by
GPT-5 mini
AI
I don’t have the full diagram or all given values, so I’m missing which angle is 40° and which angle/side the 310 in corresponds to. Can you either upload the picture or tell me:
- Which vertex has the 40° angle (A, B, or C)?
- Which side is c = 310 in (the side opposite which angle)?
- Any other given side or angle?
How to solve once that information is known
- If 40° = ∠C and c = 310 is the side opposite C, and you are given ∠B (or another angle), use the Law of Sines:
b = c * sin(B) / sin(C).
- If 40° is the included angle between sides b and c and you know the third side a, use the Law of Cosines:
b^2 = a^2 + c^2 − 2ac cos(40°) (solve for b).
Example (illustration): if ∠C = 40°, c = 310 in, and ∠B = 60°, then
b = 310 * sin(60°) / sin(40°) ≈ 310 * 0.8660 / 0.6428 ≈ 418.1 in.
Send the missing pieces (or the picture) and I’ll compute b exactly.
- Which vertex has the 40° angle (A, B, or C)?
- Which side is c = 310 in (the side opposite which angle)?
- Any other given side or angle?
How to solve once that information is known
- If 40° = ∠C and c = 310 is the side opposite C, and you are given ∠B (or another angle), use the Law of Sines:
b = c * sin(B) / sin(C).
- If 40° is the included angle between sides b and c and you know the third side a, use the Law of Cosines:
b^2 = a^2 + c^2 − 2ac cos(40°) (solve for b).
Example (illustration): if ∠C = 40°, c = 310 in, and ∠B = 60°, then
b = 310 * sin(60°) / sin(40°) ≈ 310 * 0.8660 / 0.6428 ≈ 418.1 in.
Send the missing pieces (or the picture) and I’ll compute b exactly.
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