Question

find ( mangle q ).

triangle with right angle at r, side rq = 2.7, hypotenuse qs = 3.5

write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle q = square^circ )

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle QRS \) with \( \angle R = 90^{\circ} \), \( QR = 2.7 \) (adjacent side to \( \angle Q \)) and \( QS=3.5 \) (hypotenuse). We can use the cosine function, where \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). For \( \angle Q \), \( \cos(\angle Q)=\frac{QR}{QS}=\frac{2.7}{3.5} \)

Step2: Calculate the angle

First, calculate \( \frac{2.7}{3.5}\approx0.7714 \). Then, to find \( \angle Q \), we take the inverse cosine (arccos) of \( 0.7714 \). Using a calculator, \( \angle Q=\arccos(0.7714)\approx39.6^{\circ} \) (rounded to the nearest tenth)

Answer:

\( 39.6 \)