Question

find the lengths of w, x, y, and z shown in the figure below if wy = 60. round your answers to the nearest tenth. note that the figure is not drawn to scale. 53°

Explanation:

Step1: Find \(w\) using cosine

\(\cos(53^{\circ})=\frac{w}{6}\), so \(w = 6\times\cos(53^{\circ})\approx6\times0.602 = 3.612\approx3.6\)

Step2: Find \(x\) using sine

\(\sin(53^{\circ})=\frac{x}{6}\), so \(x = 6\times\sin(53^{\circ})\approx6\times0.799 = 4.794\approx4.8\)

Step3: Use \(wy = 60\) to find \(y\)

Since \(w\approx3.6\), then \(y=\frac{60}{w}=\frac{60}{3.6}\approx16.7\)

Step4: Find \(z\) using Pythagorean theorem

\(z=\sqrt{x^{2}+y^{2}}=\sqrt{(4.8)^{2}+(16.7)^{2}}=\sqrt{23.04 + 278.89}=\sqrt{301.93}\approx17.4\)

Answer:

\(w = 3.6\)
\(x = 4.8\)
\(y = 16.7\)
\(z = 17.4\)