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In any triangle
tan A + tan B + tan C = tan A tan B tan C
Where: A = angle A, B = base, C = angle C
Solved example
Given: B = 30°, C = 45°
Find: A (angle A)
- Formula: tan(A) + tan(B) + tan(C) = tan(A)·tan(B)·tan(C)
- Rearranged for A: A = atan((tan(B) + tan(C))/(tan(B)·tan(C) - 1))
- Substitute the values: A = atan((tan(30°) + tan(45°))/(tan(30°)·tan(45°) - 1))
- Result: A = -1.308997 rad = -75°
Answer: A = -1.308997 rad = -75°
Calculator
How to calculate In any triangle
- Write down the formula: tan A + tan B + tan C = tan A tan B tan C.
- Note the known values (B, C).
- Substitute them and simplify to find A.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for In any triangle?
The formula is tan A + tan B + tan C = tan A tan B tan C, where A = angle A, B = base, C = angle C.
What is In any triangle when B = 30°, C = 45°?
A = -1.308997 rad = -75°. Substitute the values into tan A + tan B + tan C = tan A tan B tan C and simplify.