In the diagram, TX is perpendicular to UW, |UX| = 1cm and |TX| = |WX| = \(\sqrt{3}\)cm. Find UTW
Attached Figure / Diagram
A
135o
B
105o
C
75o
D
60o
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
In \(\Delta\) UXT, tan\(\alpha\) = \(\frac{1}{\sqrt{3}}\)
\(\alpha\) = tan-1(\(\frac{1}{\sqrt{3}}\))
= 30o
In \(\Delta\)WXT, tan\(\beta\) \(\frac{\sqrt{3}}{\sqrt{3}}\) = 1
\(\beta\) = tan-1(1) = 45o
Hence, o + 45o = 75o
Source: Myschool Past Questions Archive (Record #46175)