Question

Which of the following trigonometric equations is valid for the side measurements x inches, diagonal measurement y inches, and angle θ in a right-angled triangle?

a) sin(θ) = x/y
b) tan(θ) = x/y
c) cos(θ) = x/y
d) sin(θ) = y/x

Answer 1

The valid trigonometric equation for a right-angled triangle with side measurements x inches, diagonal measurement y inches, and angle θ is sin(θ) = y/x.

Step-by-step explanation:

In a right-angled triangle with side measurements x inches, diagonal measurement y inches, and angle θ, the valid trigonometric equation is option d) sin(θ) = y/x.

This is because the sine of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is y inches and the hypotenuse is x inches. Therefore, the correct equation is sin(θ) = y/x.

For example, if the angle θ is 30 degrees, the equation would be sin(30) = y/x.