Question

find qr.
write your answer as an integer or as a decimal rounded to the nearest tenth.
qr =
submit
find trigonometric functions of special angles
not feeling ready yet? these c
work it out

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle QRS \) with \( \angle Q = 90^{\circ} \), \( \angle S=35^{\circ} \) and hypotenuse \( SR = 7 \). We want to find the length of \( QR \), which is the side opposite to \( \angle S \). The sine of an angle in a right - triangle is defined as \( \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(35^{\circ})=\frac{QR}{SR} \).

Step2: Substitute values and solve for \( QR \)

We know that \( SR = 7 \) and \( \theta = 35^{\circ} \). Substituting these values into the sine formula, we get \( QR=SR\times\sin(35^{\circ}) \).
We know that \( \sin(35^{\circ})\approx0.5736 \) (using a calculator). Then \( QR = 7\times0.5736 = 4.0152\approx4.0 \) (rounded to the nearest tenth).

Answer:

\( 4.0 \)