Question 25

ΔABC is right angled at B. If $$cot A = \frac{8}{15}$$, then what is the value of $$cos C$$ ?

Solution

Given : $$\cot A$$ = $$\frac{8}{15}$$

Also, $$\cot A=\frac{AB}{BC}=\frac{8}{15}$$

Let AB = 8 cm and BC = 15 cm

Thus, in $$\triangle$$ ABC,

=> $$(AC)^2=(AB)^2+(BC)^2$$

=> $$(AC)^2=(8)^2+(15)^2$$

=> $$(AC)^2=64+225=289$$

=> $$AC=\sqrt{289}=17$$ cm

To find : $$\cos C=\frac{BC}{AC}$$

= $$\frac{15}{17}$$

=> Ans - (D)

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