Question 25

ΔXYZ is right angled at Y. If tanX = 15/8, then what is the value of sinZ ?

Solution

Given : $$\tan X$$ = $$\frac{15}{8}$$

Also, $$\tan X=\frac{YZ}{XY}=\frac{15}{8}$$

Let XY = 8 cm and YZ = 15 cm

Thus, in $$\triangle$$ XYZ, => $$(XZ)^2=(XY)^2+(YZ)^2$$

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

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

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

To find : $$\sin Z=\frac{XY}{XZ}$$

= $$\frac{8}{17}$$

=> Ans - (D)

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