Question

Please help me with this problem, please

Answer 1

Answer:

sin(x) = 5/13

cos(y) = 5/12

Therefore, sin(x) = cos(y)

Step-by-step explanation:

Trig ratios:

$sin(\theta)=\dfrac{O}{H}\\\\\\cos(\theta)=\dfrac{A}{H}\\\\\\tan(\theta)=\dfrac{O}{A}$

where $\theta$ is the angle, O is the measure of the side opposite the angle, A is the measure of the side adjacent to the angle and H is the hypotenuse, of a right triangle

We have been given the measures of the two legs, so we can find the measure of the hypotenuse by using Pythagoras' Theorem $a^2+b^2=c^2$

(where a and b are the legs and c is the hypotenuse of a right triangle)

$\implies 5^2+12^2=c"\\\\\implies 169=c^2\\\\\implies c=\sqrt{169}\\\\ \implies c=13$

Now we can use the trig ratios:

$\implies sin(x)=\dfrac{5}{13}$

$\implies cos(y)=\dfrac{5}{13}$

Therefore, sin(x) = cos(y)