Question

In OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm (see Fig. 8.12). Determine the values of sin Q and cos Q.

Answer 1

Given
Op= 7 cm
OQ -PQ = 1
OQ = 1 + PQ

Act to Pythagoras theorem
( OQ) ^2 = (OP) ^2 + (PQ) ^2
(1+ PQ) ^2 = (7)^2 + (PQ) ^2
1 + (PQ) ^2 + 2PQ = 49 + (PQ) ^2

(PQ) ^2 will be canceled out

Then
1+ 2PQ = 49
2PQ = 48
PQ = 24
Then
OQ = 1+ 24
= 25
Now
sinQ = perpendicular/ hypotenuse
= OP/OQ
= 7/25
Cos Q = base / hypotenuse
= PQ / OQ
= 24/25
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Answer 2

$OQ^{2}=OP^{2}+PQ^{2}\\ OQ^{2}=7^{2} +(OQ-1)^{2}\\OQ^{2}=49+OQ^{2}-1\\\\\\Hope\\ this \\answer \\helps \\you$