Answer: 13 units
Step-by-step explanation:
Given: A right triangle has a horizontal leg =12 units
The opposite angle to the horizontal leg = 67.4 degrees
In trigonometry, the value of sine of an angle (x) in a right triangle is given by:-
[tex]\sin x=\frac{\text{side opposite to x}}{\text{Hypotenuse}}[/tex]
Since, the hypotenuse is labeled as r.
Then , we have
[tex]\sin(67.4^{\circ})=\frac{12}{r}\\\\\Rightarrow\ r=\frac{12}{\sin (67.4^{\circ})}\\\\\Rightarrow r=\frac{12}{0.92321021711}\\\\\Rightarrow r=12.9981230467\approx13[/tex]
Hence, the value of r = 13 units.
