Question

find rs.
right triangle rqs with right angle at r, hypotenuse qs = 7, angle at s is 59 degrees.
write your answer as an integer or as a decimal rounded to the nearest tenth.
rs =
submit
work it out

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( RQS \), we know the hypotenuse \( QS = 7 \) and we need to find the adjacent side to the angle \( \angle S = 59^\circ \), which is \( RS \). The cosine function relates the adjacent side and the hypotenuse: \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \).

Step2: Apply the cosine formula

Let \( \theta = 59^\circ \), adjacent side \( = RS \), hypotenuse \( = 7 \). So \( \cos(59^\circ)=\frac{RS}{7} \). Rearranging to solve for \( RS \), we get \( RS = 7\times\cos(59^\circ) \).

Step3: Calculate the value

Using a calculator, \( \cos(59^\circ)\approx0.5150 \). Then \( RS = 7\times0.5150\approx3.6 \) (rounded to the nearest tenth).

Answer:

\( 3.6 \)