Question

solve the right triangle. round your answers to the nearest tenth. a = \\(\square^\circ\\) b = \\(\square\\) c = \\(\square\\) (triangle with angle 50°, side 16, right angle, labeled a, b, c)

Explanation:

Step1: Find angle A

In a right triangle, the sum of angles is \(180^\circ\), and one angle is \(90^\circ\), another is \(50^\circ\). So \(A = 180^\circ - 90^\circ - 50^\circ = 40^\circ\).

Step2: Find side b

We know the adjacent side to \(50^\circ\) is 16, and \(b\) is opposite to \(50^\circ\). Using tangent: \(\tan(50^\circ)=\frac{b}{16}\), so \(b = 16\times\tan(50^\circ)\approx16\times1.1918\approx19.1\).

Step3: Find side c

Using cosine: \(\cos(50^\circ)=\frac{16}{c}\), so \(c=\frac{16}{\cos(50^\circ)}\approx\frac{16}{0.6428}\approx24.9\).

Answer:

\(A = 40^\circ\), \(b \approx 19.1\), \(c \approx 24.9\)