Question

find ( mangle r ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle r=) 。
submit
work it out
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Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(RQS\), \(\angle Q = 90^{\circ}\). We know the adjacent side to \(\angle R\) (\(QR = 3\)) and the hypotenuse (\(RS=4\)). We use the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos R=\frac{QR}{RS}\).

Step2: Substitute the values

Substitute \(QR = 3\) and \(RS = 4\) into the cosine formula. Then \(\cos R=\frac{3}{4}=0.75\).

Step3: Find the angle

To find \(R\), we use the inverse cosine function. \(R=\cos^{- 1}(0.75)\). Using a calculator, \(R\approx41.4^{\circ}\).

Answer:

\(41.4\)