Question 25

In ΔABC measure of angle B is 90°. If cosecA = 13/12, and AB = 10cm, then what is the length (in cm) of side AC?

Solution

Given : AB = 10 cm and cosec A = 13/12

=> $$cosecA=\frac{AC}{BC}=\frac{13}{12}$$

Let $$AC=13x$$ and $$BC=12x$$

In right triangle ABC, => $$(AC)^2=(AB)^2+(BC)^2$$

=> $$(13x)^2=(10)^2+(12x)^2$$

=> $$169x^2-144x^2=100$$

=> $$25x^2=100$$

=> $$x^2=\frac{100}{25}=4$$

=> $$x=\sqrt4=2$$

$$\therefore$$ $$AC=13\times2=26$$ cm

=> Ans - (D)

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