In the diagram, TX is perpendicular to UW, |UX| = 1cm and |TX| = |WX|

MATHEMATICS

WAEC 2016

In the diagram, TX is perpendicular to UW, |UX| = 1cm and |TX| = |WX| = √3cm. Find UTW

A. 135°
B. 105°
C. 75°
D. 60°

Correct Answer: C. 75°

Explanation

In \(\Delta\) UXT, tan\(\alpha\) = \(\frac{1}{\sqrt{3}}\)

\(\alpha\) = tan^-1(\(\frac{1}{\sqrt{3}}\))

= 30^o

In \(\Delta\)WXT, tan\(\beta\) \(\frac{\sqrt{3}}{\sqrt{3}}\) = 1

\(\beta\) = tan^-1(1) = 45^o

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

= 30^o + 45^o = 75^o

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