Question

using trig to find a side
question
video examples
solve for x. round to the nearest tenth, if
necessary.
answer
attempt 1 out of 3
x = submit answer

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) (\(\angle B = 90^{\circ}\)), we know the adjacent side (\(BC = 44\)) to the angle \(\angle C=46^{\circ}\) and we want to find the opposite side (\(AB=x\)). The tangent ratio is defined as \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan C=\frac{AB}{BC}\).

Step2: Substitute the values into the tangent formula

Since \(\theta = 46^{\circ}\), \(BC = 44\), and \(AB=x\), we have \(\tan(46^{\circ})=\frac{x}{44}\).

Step3: Solve for \(x\)

Multiply both sides of the equation by \(44\): \(x = 44\times\tan(46^{\circ})\).
We know that \(\tan(46^{\circ})\approx1.0355\) (using a calculator). Then \(x=44\times1.0355 = 45.562\).

Answer:

\(45.6\)