Question

find a value of θ in 0°, 90° that satisfies the statement. leave the answer in decimal degrees rounded to three decimal places, if necessary
tan θ = 1.522

a. 33.306°
b. 123.306°
c. 56.694°
d. 236.694°

Explanation:

Step1: Recall the inverse tangent function

To find \( \theta \) when \( \tan\theta = 1.522 \), we use the inverse tangent function, \( \theta=\arctan(1.522) \).

Step2: Calculate the value using a calculator

Using a calculator in degree mode, we find \( \arctan(1.522)\approx56.694^\circ \). We also note that the range of \( \theta \) is \( [0^\circ, 90^\circ] \), and options B (\( 123.306^\circ \)) and D (\( 236.694^\circ \)) are outside this range. Option A (\( 33.306^\circ \)) is the arctangent of a different value (since \( \tan(33.306^\circ)\approx0.65 \) approximately, not 1.522).

Answer:

C. \( 56.694^\circ \)