Question 25

In ΔXYZ measure of angle Y is 90° . If sinX = 4/5, and XY = 6cm, then what is the length (in cm) of side YZ?

Solution

Given : XY = 6 cm and sinX = 4/5 ---------(i)

To find : YZ = ?

Solution : $$cosX=\sqrt{1-sin^2X}$$

=> $$cosX=\sqrt{1-\frac{16}{25}}=\sqrt{\frac{9}{25}}=\frac{3}{5}$$ ----------(ii)

Dividing equation (i) by (ii), => $$tanX=\frac{4}{3}$$

In right $$\triangle$$ XYZ,

=> $$tan(X)=\frac{YZ}{XY}$$

=> $$\frac{4}{3}=\frac{YZ}{6}$$

=> $$YZ=\frac{4}{3}\times6=8$$ cm

=> Ans - (C)

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