The sine of the angle is the ratio between the lengths of the opposite side and the hypotenuse.
sin x^(∘) = Length of leg opposite to the x^(∘) angle/Length of hypotenuse
In our triangle, we have that the length of the opposite leg to the x^(∘) angle is 26 34 and the length of the hypotenuse is 81.
The sine of the angle is 107324. Now, to isolate x^(∘) we will use the inverse function of sin.
sin x^(∘)=107/324 ⇔ x^(∘)=sin ^(- 1)107/324
Let's use a calculator to find the value of sin ^(- 1) 107324. First, we will set our calculator into degree mode. To do so, we need to push MODE, select Degree instead of Radian in the third row, and push ENTER. Next, we push 2ND followed by SIN, introduce the value 107324, and press ENTER.
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The value of x^(∘) is about 19.3^(∘).
Value of y
We can find the value of y using the cosine ratio.
The cosine of the angle is the ratio between the lengths of the adjacent side and the hypotenuse.
cos y = Length of leg adjacent to they^(∘)angle/Length of hypotenuse
In our triangle, we have that the length of the adjacent leg to the y^(∘) angle is 26 34 and the length of the hypotenuse is 81.
The cosine of the angle is 107324. Now, to isolate y^(∘) we will use the inverse function of cos.
cos y^(∘)=107/324 ⇔ y^(∘)=cos ^(- 1)107/324
Similar as before, we will use a calculator to find the value of cos ^(- 1) 107324. Let's do it!
