Question

solve for x. round to the nearest tenth.

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle with hypotenuse 28, angle 67° (wait, maybe the angle is 67? Wait, the triangle has a right angle, angle at the base is, let's see, the side x is opposite? Wait, no, wait, the hypotenuse is 28, angle at the base is, let's check: in a right triangle, sine of an angle is opposite over hypotenuse. Wait, maybe the angle is 67 degrees? Wait, the diagram: right angle, one angle is 67°, hypotenuse 28, x is the opposite side to the 67° angle? Wait, no, wait, maybe the angle is 67°, so \(\sin(67^\circ)=\frac{x}{28}\)

Step2: Solve for x

Multiply both sides by 28: \(x = 28\times\sin(67^\circ)\)
Calculate \(\sin(67^\circ)\approx0.9205\)
So \(x\approx28\times0.9205 = 25.774\approx25.8\) (rounded to nearest tenth)

Wait, maybe I misread the angle. Wait, the diagram: the angle at the base is 67°, hypotenuse 28, x is the opposite side. So sine of 67° is opposite over hypotenuse. So yes, \(x = 28\sin(67^\circ)\approx25.8\)

Answer:

\(25.8\)