Question

label the sides and angle and calculate the missing values in the triangle
a = 1.88
θ =
h =
o = 1.37

Explanation:

Step1: Find the angle \(\theta\)

Use the tangent function \( \tan\theta=\frac{O}{A}\).
Given \(A = 1.88\) and \(O=1.37\), then \( \tan\theta=\frac{1.37}{1.88}\).
\(\theta=\arctan(\frac{1.37}{1.88})\approx36.1^{\circ}\)

Step2: Find the hypotenuse \(H\)

Use the Pythagorean theorem \(H=\sqrt{A^{2}+O^{2}}\).
Substitute \(A = 1.88\) and \(O = 1.37\) into the formula:
\(H=\sqrt{(1.88)^{2}+(1.37)^{2}}=\sqrt{3.5344 + 1.8769}=\sqrt{5.4113}\approx2.33\)

Answer:

\(\theta\approx36.1^{\circ}\), \(H\approx2.33\)