Given: A right triangle with a side and included angle
To Determine: The value of the unknown x
Solution:
In a right triangle, the side facing the right angle is the hypothenuse, the side facing the given angle is the opposite and the other side is the adjacent.
This is as shown in the given figure as
Using trigonometry identities
[tex]\begin{gathered} sin\theta=\frac{opposite}{hypothenuse} \\ cos\theta=\frac{adjacent}{hypothenuse} \\ tan\theta=\frac{opposite}{adjacent} \\ Therefore \\ sin46^0=\frac{24}{x} \end{gathered}[/tex][tex]\begin{gathered} x\times sin46^0=24 \\ x=\frac{24}{sin46^0} \\ x=33.3639 \\ x\approx33.4(nearest\text{ tenth\rparen} \end{gathered}[/tex]
Hence, the value of x is 33.4
