Multiple choice

Two angles of a triangle are ${\cot ^{ - 1}}2$ and ${\cot ^{ - 1}}3$. Then the third angle

  1. $\dfrac{\pi }{4}$
  2. $\dfrac{{3\pi }}{4}$
  3. $\dfrac{{\pi }}{6}$
  4. $\dfrac{{\pi }}{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A = cot^-1(2) and B = cot^-1(3). Then tan(A) = 1/2 and tan(B) = 1/3. tan(A+B) = (1/2 + 1/3) / (1 - 1/6) = (5/6) / (5/6) = 1. So A+B = 45 degrees (pi/4). The third angle C = 180 - 45 = 135 degrees (3pi/4).

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