Question

the sides and angle and calculate the missing values in the triangle:
1.93 sin(38.5) = 1.201453249
tan^{-1}(\frac{1.34}{1.76}) = 37.28432644
tan^{-1}(\frac{1.76}{1.34}) = 52.71567356
h =
o = 1.34
θ = 37.3
a = 1.76

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin\theta=\frac{O}{H}\), where \(O\) is the length of the opposite side, \(H\) is the length of the hypotenuse, and \(\theta\) is the given angle. We can rewrite the formula for \(H\) as \(H = \frac{O}{\sin\theta}\).

Step2: Substitute the values

Given \(O = 1.34\) and \(\theta=37.3^{\circ}\). First, find \(\sin(37.3^{\circ})\). Using a calculator, \(\sin(37.3^{\circ})\approx0.606\). Then \(H=\frac{1.34}{\sin(37.3^{\circ})}\).

Step3: Calculate the value of \(H\)

\(H=\frac{1.34}{0.606}\approx2.21\)

Answer:

\(H\approx2.21\)