Question

label the sides and angle and calculate the missing values in the triangle:
a =
θ = 35.9°
o = 1.81
h =

Explanation:

Step1: Use trigonometric ratio for \(\sin\theta\)

We know that \(\sin\theta=\frac{O}{H}\), where \(O = 1.81\) and \(\theta = 35.9^{\circ}\). So, \(H=\frac{O}{\sin\theta}\).

Step2: Calculate \(H\)

Substitute \(O = 1.81\) and \(\theta = 35.9^{\circ}\) into the formula. \(\sin(35.9^{\circ})\approx0.586\). Then \(H=\frac{1.81}{0.586}\approx3.09\).

Step3: Use trigonometric ratio for \(\tan\theta\)

We know that \(\tan\theta=\frac{O}{A}\), so \(A = \frac{O}{\tan\theta}\).

Step4: Calculate \(A\)

\(\tan(35.9^{\circ})\approx0.721\). Then \(A=\frac{1.81}{0.721}\approx2.51\).

Answer:

\(A = 2.51\), \(H = 3.09\)