Question

solve for x in the triangle. round your answer to the nearest tenth.
triangle image: right triangle with one acute angle 46°, adjacent side to 46° is 7, opposite side is x
x = blank box

Explanation:

Step1: Identify trigonometric ratio

In a right triangle, \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 46^\circ\), opposite side is \(x\), adjacent side is \(7\). So \(\tan(46^\circ)=\frac{x}{7}\).

Step2: Solve for \(x\)

Multiply both sides by \(7\): \(x = 7\times\tan(46^\circ)\). Calculate \(\tan(46^\circ)\approx1.0355\), then \(x\approx7\times1.0355 = 7.2485\). Round to nearest tenth: \(x\approx7.2\).

Answer:

\(x\approx7.2\)