Question

NO LINKS!!! URGENT HELP PLEASE!!​

Answer 1

A) sin 59 = cos 31

Explanation:

hypotenuse² = x² + 17²

⇒ hypotenuse = √(x² + 17²)

The other angle is 180-90-31 = 59

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

sin 59 = x / √(x² + 17²)

cos 31 = x / √(x² + 17²)

so sin 59 = cos 31

Answer 2

A) sin 59° = cos 31°

Explanation:

The interior angles of a triangle sum to 180°. Therefore, the measure of the missing angle is:

`180^(\circ)-90^(\circ)-31^(\circ)=\boxed{59^(\circ)}`

Trigonometric ratios are mathematical relationships that define the ratios between the sides of a right triangle and the angles within that triangle. The sine and cosine trigonometric ratios are:

`\boxed{\begin{minipage}{9.4 cm}\underline{Sine and Cosine trigonometric ratios} \\\\$\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}`

The legs of the given right triangle are labelled "x" and "17". The hypotenuse is not labelled. Therefore, as both the sine and cosine ratios include the hypotenuse, sin 59° and cos 31° cannot equal x/17.

Let the hypotenuse be "H". Therefore, using the sine and cosine ratios, we can say that:

`\sin 59^(\circ)=(x)/(H)`

`\cos 31^(\circ)=(x)/(H)`

Therefore, the only correct equation from the given answer options is:

`\large\boxed{\sin 59^(\circ)=\cos 31^(\circ)}`