ANSWER
The exact value is 24√3
The approximate value is 41.6 to the nearest tenth.
x=52.1 units.
EXPLANATION
Let the blue dotted line be h units.
This line is opposite to the 60° angle.
The side length of the triangle which is 24 units is adjacent to the 60° angle.
So we use the tangent ratio,
[tex] \tan(60 \degree) = \frac{opposite}{adjacent} [/tex]
[tex] \tan(60 \degree) = \frac{h}{24} [/tex]
[tex] \sqrt{3} = \frac{h}{24} [/tex]
[tex]h = 24 \sqrt{3} [/tex]
This is the exact value.
[tex]h = 41.6[/tex]
This is that approximate value to the nearest tenth.
To find the side length , x, we need to use the second triangle.
[tex] \sin(53\degree) = \frac{h}{x} [/tex]
[tex] \sin(53\degree) = \frac{41.6}{x} [/tex]
[tex]x = \frac{41.6}{\sin(53\degree)} [/tex]
[tex]x = 52.1[/tex]
