Answer: x = 10tan(51°) or x ≈ 12.34897
Step-by-step explanation:
We are given a right triangle, an angle, and two leg measurements. To find the missing side, x, we will use trigonometric properties. We are not given the hypotenuse, so we will utilize the tangent function.
Tangent:
[tex]\displaystyle tan\theta=\frac{\text{opposite}}{\text{adjacent}}[/tex]
Substitute known values:
[tex]\displaystyle tan(51\°)= \frac{x}{10}[/tex]
Multiply both sides of the equation by 10:
[tex]\displaystyle 10tan(51\°)=x[/tex]
Compute:
[tex]\displaystyle x\approx 12.34897[/tex]
