Question

find qr.
triangle image with right angle at r, pr=2, angle at p is 68°
write your answer as an integer or as a decimal rounded to the nearest tenth.
qr =
submit

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle PRQ \) with \( \angle R = 90^{\circ} \), \( PR = 2 \), and \( \angle P=68^{\circ} \). We want to find \( QR \). We can use the tangent function, which is defined as \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle P \), the opposite side to \( \angle P \) is \( QR \) and the adjacent side is \( PR \). So \( \tan(68^{\circ})=\frac{QR}{PR} \).

Step2: Solve for \( QR \)

We know that \( PR = 2 \) and \( \tan(68^{\circ})\approx2.475 \). Substituting the values into the formula \( QR = PR\times\tan(68^{\circ}) \), we get \( QR=2\times\tan(68^{\circ}) \).
\( QR = 2\times2.475 = 4.95\approx5.0 \) (rounded to the nearest tenth)

Answer:

\( 5.0 \)