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Answer:  θ = 48.2°

Step-by-step explanation:

The left side of the given triangle is a right triangle with base (adjacent to θ) = 2 and hypotenuse = 3

[tex]\cos \theta = \dfrac{adjacent}{hypotenuse}\\\\\\\cos \theta=\dfrac{2}{3}\\\\\\\theta =\cos^{-1}\bigg(\dfrac{2}{3}\bigg)\\\\\\\theta = 48.1896[/tex]

rounded to three significant digits = 48.2°

The measure of angle theta is 48.2 degrees.

What is cosine of an angle?

In a right angled triangle, the cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse.

According to the given question

We have a right triangle

Let the be ABC in which ∠ACE = θ

And,  AE is a perpendicular bisector so CE = 4/2

Now in right angled triangle ACE, the cosine of θ is given by

cosθ = length of the adjacent side/ hypotenuse

⇒ cosθ = [tex]\frac{CE}{AC}[/tex]

⇒cosθ = [tex]\frac{2}{3}[/tex]

⇒ θ = [tex]cos^{-1}( \frac{2}{3} )[/tex]

⇒ θ = 48.2 degrees

Hence, the measure of angle theta is 48.2 degrees.

Learn more about cosine of an angle here:

https://brainly.com/question/9932656

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