To find the measure of the angle [tex]\( \angle W \)[/tex] given that [tex]\( \tan W = 3.52 \)[/tex], we can follow these steps:
1. Understanding the Problem: We know that the tangent of an angle [tex]\( W \)[/tex] is given as [tex]\( 3.52 \)[/tex]. We need to find the angle [tex]\( W \)[/tex] in degrees to the nearest tenth.
2. Using the Inverse Tangent Function: The tangent function [tex]\( \tan \)[/tex] relates an angle in a right triangle to the ratio of the opposite side to the adjacent side. To find the angle [tex]\( W \)[/tex], we use the inverse tangent function (often written as [tex]\( \arctan \)[/tex] or [tex]\( \tan^{-1} \)[/tex]).
3. Calculation in Radians: First, we find [tex]\( W \)[/tex] in radians. Using the inverse tangent function:
[tex]\[
W = \arctan(3.52)
\][/tex]
4. Converting Radians to Degrees: The angle [tex]\( W \)[/tex] calculated in radians can be converted to degrees. The conversion factor between radians and degrees is [tex]\( 180 / \pi \)[/tex].
5. Approximation and Rounding: After converting to degrees, we round the result to the nearest tenth of a degree.
Given the above approach, the calculations yield the following:
- The angle in radians is approximately [tex]\( 1.2939981681629065 \)[/tex] radians.
- Converting this to degrees gives approximately [tex]\( 74.14063373339431 \)[/tex] degrees.
- Rounding this to the nearest tenth, we get [tex]\( 74.1^\circ \)[/tex].
Thus, the measure of [tex]\( \angle W \)[/tex] to the nearest tenth of a degree is:
[tex]\[
\boxed{74.1^\circ}
\][/tex]
So, the correct option is:
d. about [tex]\( 74.1^\circ \)[/tex]
