Jamb Question: In the figure if QR= 8cm, find the length of PS.

SOLUTION (from Samimath.com)

We have two Right angled triangles with a common side PR. We will first find the common side using trianglePQR (because we have all we need to find trigonometrical ratio sine)and then use its value to find side PS.

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In trianglePQR:
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Applying trigonometrical ratios
Sin 60° = PR/QR

Sin 60° = PR/8
Making PR the subject of the formula:
PR = 8 × Sin 60°
But Sin 60° = √3/2
Therefore,
PR = 8 × √3/2
= 4√3

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In trianglePSR:
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angle S + 90 + 45 = 180
angle S = 180 – 135
angle S = 45

Applying trigonometrical ratios

Sin 45° = PR/PS
= (4√3)/PS
Making PS the subject of the formula

PS = (4√3)/Sin 45°

But, Sin 45° = 1/√2

Then PS = 4√3 ÷ 1√2
= 4√3 × √2/1
= 4√(3×2)
= 4√6cm

Bravo! The answer is 4√6 cm.

If you have any questions kindly ask them here http://samimath.com/forums/forum/math-forum/

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Tutorial on trigonometrical ratios is here: http://samimath.com/undersranding-trigonometrical-ratios-a-simple-introduction/

Other Examples and detailed solution can be found here http://samimath.com/math-questions-and-solutions/
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