Question

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Answer 1

GIVEN:

∆XYZ, ∠Y is right angle, XZ = 17 m and YZ = 15 cm.

TO FIND:

(i) sin X

(ii) cos Z

(iii) tan X

SOLUTION:

By Pythagoras theorem,

XZ² = YZ² + XY²

17² = 15² + XY²

XY² = 17² - 15² => 289 - 225

XY² 64

XY = √64 => 8.

$\bold {(i) \: \sin(x) = \frac{opposite \: side \: of \: ∠x}{hypotenuse}} \\ \bold{ \frac{yz}{xz} = \frac{15}{17} }$

$\bold{(ii) \cos(z) = \frac{adjacent \: side \: to \: ∠z}{hypotenuse} } \\ \bold {\frac{yz}{xz} = \frac{15}{17}}$

$\bold{(iii) \tan(x) = \frac{opposite \: side \: to \: ∠x}{adjacent \: side \: to \: ∠x} } \\ \bold{\frac{yz}{xy} = \frac{15}{8} }$