Question

label the sides and angle and calculate the missing values in the triangle:

1. 10 cos(35.9) = 1.802459399

\frac{2.10}{cos(35.9)} = 3.07391603

\frac{1.96}{cos(39.1)} = 2.525622156

Explanation:

Step1: Label the sides

In a right - triangle, we can label the sides as follows:

• Let the side adjacent to the angle \(\theta = 35.9^{\circ}\) be \(A = 2.53\)
• Let the side opposite to the angle \(\theta\) be \(O\)
• Let the hypotenuse be \(H\)

Step2: Calculate the side \(O\)

We know that \(\tan\theta=\frac{O}{A}\). But if we use \(\cos\theta=\frac{A}{H}\), we first find \(H\) from \(A = 2.53\) and \(\theta = 35.9^{\circ}\). Since \(\cos\theta=\frac{A}{H}\), then \(H=\frac{A}{\cos\theta}\). Substituting \(A = 2.53\) and \(\theta = 35.9^{\circ}\), \(\cos(35.9^{\circ})\approx0.81\), \(H=\frac{2.53}{0.81}\approx3.11\)

Also, using \(\sin\theta=\frac{O}{H}\), then \(O = H\sin\theta\). Substituting \(H = 3.11\) and \(\theta = 35.9^{\circ}\), \(\sin(35.9^{\circ})\approx0.63\), \(O=3.11\times0.63 = 1.96\)

Answer:

The side adjacent \(A = 2.53\), the side opposite \(O = 1.96\), the hypotenuse \(H = 3.11\) and the angle \(\theta=35.9^{\circ}\)