Find x 58 degrees and adjacent 4.0

It would help if you indicated which side x would be so I will show you how to solve for the two remaining sides. I am assuming that your triangle is a right triangle because you mentioned the word "adjacent."

You can solve it using the trigonometric functions SOH CAH TOA. 

Let's solve for the hypotenuse which is the longest side or side opposite the right angle. 

IF X WAS THE HYPOTENUSE (H):
You have adjacent and the angle so you need to use the trigonometric function CAH because you're looking for the hypotenuse. 
Angle = 58 degrees
A = 4 units





IF X WAS THE OPPOSITE (O):
Now we solve for the opposite side using TOA and using the same given as the problem above. 







Attached is a picture of each scenario.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12