Question

Not ConnectedThunde...lt BridgeNot Connected2 (07.01 HC)answer the following question. Find the value of sin x and cosy. What relationship do the ratios of sin x® and cos yº share?

Answer 1

The given triangle is a right-angled triangle.

Consider PO is Hypotenuse.

By using the Pythagoras formula, we get

$PO^2=8^2+6^2$

$PO^2=64+36$$PO^2=100=10^2$$PO=10$

Consider the angle x:

Recall the sine formula

$\sin \theta=\frac{Opposite\text{ side}}{\text{Hypotenuse}}$

Substitute Opposite side =6 and Hypotenuse=10, we get

$\sin x^o=\frac{6}{10}$

$\sin x^o=\frac{3}{5}$$\text{Use sin }36.869=\frac{3}{5}$

$\sin x^o=\sin 36.869$$x^o=37$

Consider the angle y:

Recall the sine formula

$\sin \theta=\frac{Opposite\text{ side}}{\text{Hypotenuse}}$

Substitute Opposite side =8 and Hypotenuse=10, we get

$\sin y^o=\frac{8}{10}$

$\sin y^o=\frac{4}{5}$

$\text{Use }\sin 53.13^{}=\frac{4}{5}$

$\sin y^o=\sin \text{ 53.13}$$y^o=53^{}$

Hence the required values are

$x^o=37^o$$y^o=53^o$