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8. Introduction to Trigonometry
medium
In $\triangle$ $OPQ$, right-angled at $P$, $OP =7\, cm$ and $OQ - PQ =1\, cm$ (see $Fig.$). Determine the values of $\sin Q$ and $\cos Q$.
Option A
Option B
Option C
Option D
Solution
In $\triangle$ OPQ, we have
$OQ ^{2}= OP ^{2}+ PQ ^{2}$
i.e., $\quad(1+ PQ )^{2}= OP ^{2}+ PQ ^{2}$
i.e., $\quad 1+ PQ ^{2}+2 PQ = OP ^{2}+ PQ ^{2}$
i.e., $\quad 1+2 PQ =7^{2}$
i.e., $\quad PQ =24\,cm$ and $OQ =1+ PQ =25 \,cm$
So, $\sin Q =\frac{7}{25}$ and $\cos Q =\frac{24}{25}$
Standard 10
Mathematics
