Question

find the value of \\(\cos q\\) rounded to the nearest hundredth, if necessary.

(image of a right triangle qrs with right angle at r, sr = \\(\sqrt{21}\\), sq = \\(\sqrt{85}\\))

answer attempt 1 out of 2
\\(\cos q = \\) input box submit answer

Explanation:

Step1: Identify sides for cos Q

In right triangle QRS (right at R), cos Q = adjacent/hypotenuse. Adjacent to Q is QR; hypotenuse is QS = √85. First find QR using Pythagoras: QR = √(QS² - SR²) = √((√85)² - (√21)²) = √(85 - 21) = √64 = 8.

Step2: Calculate cos Q

cos Q = QR / QS = 8 / √85 ≈ 8 / 9.2195 ≈ 0.8677. Round to nearest hundredth: 0.87.

Answer:

0.87