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P and Q are the two points on the ground. In between them a pole AB is stood. A is tied to P and A is tied to Q. P makes an angle of \( \Large 30 ^{\circ} \) and Q makes an angle of \( \Large 45 ^{\circ} \), with the ground respectively. The length of PA is 10 mts. Find the length of AQ.

A) \( \Large 10\sqrt{2} \)mts.
B) \( \Large \sqrt{20} \)mts.
C) \( \Large 4\sqrt{5} \)mts.
D) \( \Large 5\sqrt{2} \)mts.

Correct Answer:




D) \( \Large 5\sqrt{2} \)mts.

Description for Correct answer:

\( \Large From \triangle PAB \)

\( \Large \sin 30 = \frac{AB}{AP} \)

\( \Large \frac{1}{2} = \frac{x}{10} \)

x = 5

\( \Large From \triangle ABQ \)

\( \Large \tan 45 = \frac{AB}{BQ} \)

AB = BQ

BQ = 5

\( \Large From \triangle ABQ \)

\( \Large AQ^{2} = AB^{2} + BQ^{2} \)

=\( \Large 5^{2} + 5^{2} = 50 \)

\( \Large AQ = \sqrt{50} = 5\sqrt{2} \)

Part of solved Trigonometry questions and answers : >> Elementary Mathematics >> Trigonometry

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