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Mathematics · Introduction to Trigonometry · NCERT Examples

Example 5

A complete, independently verified solution for NCERT Example 5.

Mathematics · Chapter 8 · NCERT Examples

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NCERT Example

Example 5

right triangle · trigonometric ratios

In right triangle OPQ, right-angled at P, OP = 7 cm and OQ − PQ = 1 cm. Find sin Q and cos Q.

Right triangle OPQ, right-angled at P, with OP equal to 7 centimetres.
Figure 8-12 from the supplied NCERT chapter.

Solution

Board-exam working:

Let PQ = x cm. Then OQ = x + 1 cm.

OQ2=OP2+PQ2OQ^2=OP^2+PQ^2
(x+1)2=72+x2(x+1)^2=7^2+x^2
x2+2x+1=49+x2x^2+2x+1=49+x^2
2x=48⇒x=242x=48\Rightarrow x=24
PQ=24 cm,OQ=25 cmPQ=24\text{ cm},\qquad OQ=25\text{ cm}
sin⁡Q=OPOQ=725\sin Q=\frac{OP}{OQ}=\frac7{25}
cos⁡Q=PQOQ=2425\cos Q=\frac{PQ}{OQ}=\frac{24}{25}

Final answer

sin⁡Q=725,cos⁡Q=2425\sin Q=\frac7{25},\qquad \cos Q=\frac{24}{25}