In the diagram, TX is perpendicular to UW, |UX| = 1cm and |TX| = |WX| = \(\sqrt{3}\)cm. Find UTW

In the diagram, TX is perpendicular to UW, |UX| = 1cm and |TX| = |WX| = \(\sqrt{3}\)cm. Find UTW

A.

135o

B.

105o

C.

75o

D.

60o

Correct answer is C

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, < UTW = \(\alpha\) + \(\beta\)

= 30o + 45o = 75o