Question

what are the value of x and the measure of ∠e to the nearest degree?

x = 4, m∠e = 37°
x = 8, m∠e = 31°
x = \sqrt{94}, m∠e = 31°
x = 8, m∠e = 37°

Explanation:

Step1: Use Pythagorean theorem

In right - triangle \(DFE\), by \(a^{2}+b^{2}=c^{2}\), where \(c = 10\), \(a = 6\), and \(b=x\). Then \(x=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8\).

Step2: Use trigonometric ratio

\(\sin E=\frac{DF}{DE}\), \(DF = 6\), \(DE = 10\). So \(\sin E=\frac{6}{10}=0.6\). Using the inverse - sine function \(E=\sin^{-1}(0.6)\approx37^{\circ}\)

Answer:

\(x = 8,m\angle E=37^{\circ}\) (the fourth option)