Given the right triangle in the picture, we know the measure of one of its acute angles and the length of the hypotenuse, and we need to determine the length of the side across the known angle.
To determine this length, you have to apply the trigonometric ratio of the sine, which is defined as:
[tex]\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]
Where
"θ" represents the acute angle
"opposite" refers to the side of the triangle across the acute angle
"hypotenuse" is the longest side of the triangle
For the given triangle, the sine of 21º can be expressed as follows:
[tex]\sin 21º=\frac{x}{15}[/tex]
From this expression, you can determine the value of x.
To do so, you have to multiply both sides of the expression by 15
[tex]\begin{gathered} 15\cdot\sin 21º=15\cdot\frac{x}{15} \\ 5.375=x \\ x\approx5.38 \end{gathered}[/tex]
The value of x is approximately 5.38 units
