hypotenuse=29
[tex]\sin x=\frac{20}{29}[/tex]
[tex]\cos y=\frac{20}{29}[/tex]
Explanation
Step 1
a) hypotenuse
to find the hypotenuse we can use the Pythagorean theorem ,it statse that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
so
[tex]\begin{gathered} 21^2+20^2\text{= hypotenuse}^2 \\ 441+400=\text{ hypotenuse}^2 \\ 841=\text{hypotenuse}^2 \\ taking\text{ the square root in both sides} \\ \sqrt{841}=\sqrt{(hypotenuse)^2} \\ 29=hypotenuse \end{gathered}[/tex]
so
hypotenuse=29
Step 2
now, sin x
the sin of an angle is the ratio of the opposite side ( the one in front of the angel) to the hypotenuse
[tex]\sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]
hence, replace
[tex]\sin x=\frac{20}{29}[/tex]
Step 3
finally, cos of y
the cos of an angle is the ratio of the adjancent side( the side the makes the angle) to the hypotenuse
[tex]cos\theta=\frac{adjacent\text{ side}}{hypotenuse}[/tex]
so,replace
[tex]\cos y=\frac{20}{29}[/tex]
I hope this helps you
