Standard High contrast

Trigonometry

Question 5 of 9

Sine and Cosine Rules

Question

Solve triangle \(ABC\) if \(a = 50\), \(b = 100\), and \(\angle A = 50^\circ\)

Show solution Hide solution Fully worked — 4 steps

\(a \lt b \sin A = 50 \lt 100 \sin 50^\circ = 50 \lt 77\), this satisfies the condition for a triangle with no solution.

Also, solving for \(\sin B\):

  1. Use the sine rule to solve for \(\angle B\)
    \[ \frac{a}{\sin A} = \frac{b}{\sin B} \]
  2. Substitute values of \(a\), \(b\) and \(\angle A\)
    \[ \frac{50}{\sin 50} = \frac{100}{\sin B} \]
  3. Cross multiply and solve for \(\angle B\)
    \[ \sin B = \frac{100 \sin 50}{50} \]
    \[ \sin B = 1.5321 \]
  4. Final answer

    Hence, no solution since \(\sin B \gt 1\). The sine of an angle is never greater than 1, so no triangle satisfies the conditions given.