Question

label the sides and angle and calculate the missing values in the triangle: o = h = 2.78 θ = ° a = 2.20

Explanation:

Step1: Calculate the angle \(\theta\)

Use the cosine function \(\cos\theta=\frac{A}{H}\).
Substitute \(A = 2.20\) and \(H=2.78\) into the formula: \(\cos\theta=\frac{2.20}{2.78}\).

$$ \cos\theta\approx0.7914 $$

Then \(\theta=\cos^{- 1}(0.7914)\approx37.7^{\circ}\)

Step2: Calculate the side \(O\)

Use the Pythagorean theorem \(O=\sqrt{H^{2}-A^{2}}\).
Substitute \(A = 2.20\) and \(H = 2.78\) into the formula:

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Answer:

\(O\approx1.70\), \(\theta\approx37.7^{\circ}\)