Question

1. approximate the angles measures that correspond to the following quotients:

a. adjacent leg ÷ hypotenuse = 0.966
b. opposite leg ÷ hypotenuse = 0.469
c. adjacent leg ÷ hypotenuse = 0.309
d. opposite leg ÷ adjacent leg = 1.036
the angle measures that correspond to the ratios

Explanation:

Step1: Use arccos for adjacent/hypotenuse

$\theta = \arccos(0.966)$

Step2: Calculate angle for part a

$\theta \approx 15^\circ$

Step3: Use arccos for adjacent/hypotenuse

$\theta = \arccos(0.469)$

Step4: Calculate angle for part b

$\theta \approx 62^\circ$

Step5: Use arccos for adjacent/hypotenuse

$\theta = \arccos(0.309)$

Step6: Calculate angle for part c

$\theta \approx 72^\circ$

Step7: Use arctan for opposite/adjacent

$\theta = \arctan(1.036)$

Step8: Calculate angle for part d

$\theta \approx 46^\circ$

Answer:

a. $15^\circ$
b. $62^\circ$
c. $72^\circ$
d. $46^\circ$