HRHRHRHRHR's answer to mary's Secondary 3 E Maths Singapore question.
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(a) Apply Pythagoras Theorem since this is a right angle triangle.
(b) Recognise that 90 - theta is just angle QRP, and then use TOA CAH SOH rule to find tan QRP, which is PQ/PR.
(c) Recognise that angle PRS and angle QRP are supplementary angles, and angle PRS is obtuse. When finding cosine (or any trigonometric function like sin and tan) for angles bigger than 90 degrees, you want to look at the basic angle. In this case, the basic angle of angle PRS is QRP. Since PRS is between 90 and 180 degrees, cos PRS will be negative. Therefore cos PRS will be negative of cos QRP. (This overlaps slightly with A Math knowledge as well yea)
Leave a comment if you still need more help / clarifications!
(b) Recognise that 90 - theta is just angle QRP, and then use TOA CAH SOH rule to find tan QRP, which is PQ/PR.
(c) Recognise that angle PRS and angle QRP are supplementary angles, and angle PRS is obtuse. When finding cosine (or any trigonometric function like sin and tan) for angles bigger than 90 degrees, you want to look at the basic angle. In this case, the basic angle of angle PRS is QRP. Since PRS is between 90 and 180 degrees, cos PRS will be negative. Therefore cos PRS will be negative of cos QRP. (This overlaps slightly with A Math knowledge as well yea)
Leave a comment if you still need more help / clarifications!
Date Posted:
1 year ago
Thank you
Could you please explain why 90-theta is QRP?
Hi, angle sum within the triangle is 180 degrees. So angle QRP + the right angle + theta = 180 degrees. You can then further simplify this into QRP + theta = 90 degrees, and subsequently this leads to angle QRP = 90 degrees - theta
Thank you
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