Question

13
In a AABC, angleB = 90°, AB = 5 cm and (BC + AC) = 25 cm. Find
the values of sin A, cos A, cosec C and sec C.
​

Answer 1

LET BC = X

BC + AC = 25 cm

x + AC = 25

AC = 25 - X

IN TRIANGLE ABC ,  BY PYTHAGOROUS THEOREM

$AC^{2}=AB^{2} + BC^{2}$

$(25-x)^{2} = 5^{2} +x^{2}$

$625+x^{2} -50x=25+x^{2}$

50x=600

⇒x=12.

∴ BC=12cm, AC=13cm and AB=5cm.

      $SIN A = \frac{BC}{AC\\ } =\frac{12}{13} \\ COSA=\frac{AB}{AC} =\frac{5}{13}\\ Cosec C=\frac{AC}{AB} =\frac{13}{5} \\ SecC=\frac{AC}{BC} =\frac{13}{12}$

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