Question

solve for x. round to the nearest tenth, if necessary.
triangle with vertices a, b, c (right angle at b), ab = 12, angle at c = 61°, bc = x
answer attempt 1 out of 2
x = blank subr

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(ABC\), \(\angle C = 61^\circ\), \(AB = 12\) (opposite to \(\angle C\)), and \(BC = x\) (adjacent to \(\angle C\)). We use the tangent function: \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So \(\tan(61^\circ)=\frac{AB}{BC}=\frac{12}{x}\).

Step2: Solve for \(x\)

Rearrange the formula: \(x = \frac{12}{\tan(61^\circ)}\). Calculate \(\tan(61^\circ)\approx1.8040\). Then \(x=\frac{12}{1.8040}\approx6.7\).

Answer:

\(6.7\)