Question

solve triangle abc. (if an answer does not exist, enter dne. round your answers to one decimal place.)
a = 68, c = 50, ∠c = 53°
∠a =
∠b =
b =

Explanation:

Step1: Use the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{c}{\sin C}\). We know \(a = 68\), \(c = 50\), and \(C=53^{\circ}\). So \(\sin A=\frac{a\sin C}{c}\).
Substitute the values: \(\sin A=\frac{68\times\sin(53^{\circ})}{50}\).
Since \(\sin(53^{\circ})\approx0.7986\), then \(\sin A=\frac{68\times0.7986}{50}=\frac{54.3048}{50}=1.0861\).

Step2: Check for the existence of the triangle

Since the range of the sine function is \([- 1,1]\), and \(\sin A = 1.0861>1\), no such triangle \(ABC\) exists.

Answer:

\(\angle A\) does not exist (DNE), \(\angle B\) does not exist (DNE), \(b\) does not exist (DNE)