In the diagram above, PR is perpendicular from P to QS, PQ = 2cm, QR = 1cm and PR = RS. what is the size of the angle QPS?
Attached Figure / Diagram
A
135o
B
105o
C
90o
D
75o
E
60o
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\Delta RPS\) = Isosceles triangle
\(\therefore < RPS = \frac{180^\circ - 90^\circ}{2}\) = 45^\circ
In \(\Delta QPR\),\(\sin < QPR = \frac{1}{2}\) = 30^\circ
\(\therefore < QPS = 30^\circ + 45^\circ = 75^\circ\)
Source: Myschool Past Questions Archive (Record #22208)