GIVEN:
We are given a right angled triangle with sides as shown.
Required;
We are required to solve for the missing side, x.
Step-by-step solution;
For any given right angled triangle, we have three sides labeled in relation to the reference angle. These are shown below;
The side facing the reference angle is the opposite
The side facing the 90 degree angle is the hypotenuse
The side that lies between the reference angle and the 90 degree angle is the adjacent.
From the information given, we have the following;
[tex]\begin{gathered} Reference\text{ }angle=43\degree \\ Opposite=x \\ Adjacent=56 \end{gathered}[/tex]
We shall now use the trig ratio;
[tex]tan\theta=\frac{opposite}{adjacent}[/tex]
We now have;
[tex]\begin{gathered} tan43\degree=\frac{x}{56} \\ \\ Now\text{ }we\text{ }cross\text{ }multiply: \\ \\ 56\times tan43=x \\ \\ 56\times0.932515086138=x \\ \\ 52.2208448237=x \end{gathered}[/tex]
Rounded to the nearest tenth, we now have;
ANSWER:
[tex]x=52.2[/tex]
