Question

13,219 Learners found this answer helpful

find qr.
write your answer as an integer or as a decimal rounded to the nearest tenth.
$qr = \square$

Explanation:

Step1: Identify trigonometric ratio

We have right triangle \(RSQ\), with \(\angle R = 76^\circ\), opposite side \(RS = 0.5\) to \(\angle Q\), and \(QR\) is the hypotenuse. Use cosine:
\(\cos(76^\circ) = \frac{RS}{QR}\)

Step2: Rearrange to solve for \(QR\)

Rearrange the formula to isolate \(QR\):
\(QR = \frac{RS}{\cos(76^\circ)}\)

Step3: Substitute values and calculate

Substitute \(RS = 0.5\) and \(\cos(76^\circ) \approx 0.2419\):
\(QR = \frac{0.5}{0.2419} \approx 2.1\)

Answer:

2.1