Question

solve the right triangle. round your answers to the nearest tenth. triangle image with right angle, angle 50°, hypotenuse 30, sides a, b, angle b b = ° a = b =

Explanation:

Step1: Find angle B

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

Step2: Find side a (opposite to \(50^\circ\))

Using sine function: \(\sin(50^\circ)=\frac{a}{30}\), so \(a = 30\times\sin(50^\circ)\). Calculate \(\sin(50^\circ)\approx0.7660\), then \(a\approx30\times0.7660 = 22.98\approx23.0\) (rounded to nearest tenth).

Step3: Find side b (adjacent to \(50^\circ\))

Using cosine function: \(\cos(50^\circ)=\frac{b}{30}\), so \(b = 30\times\cos(50^\circ)\). Calculate \(\cos(50^\circ)\approx0.6428\), then \(b\approx30\times0.6428 = 19.284\approx19.3\) (rounded to nearest tenth).

Answer:

\(B = 40^\circ\), \(a\approx23.0\), \(b\approx19.3\)