Question

the measure of an angle is given. is this angle smaller or larger than a right angle?
θ = 5/9
select the correct answer below and fill in the answer box to complete your choice.
(simplify your answer. round to three decimal places as needed.)
a. the angle is smaller than a right angle because 5/9 is approximately, which is less than π/2 ≈.
b. the angle is larger than a right angle because 5/9 is approximately, which is greater than π/2 ≈.

Explanation:

Step1: Calculate the decimal - value of $\frac{5}{9}$

$\frac{5}{9}\approx0.556$

Step2: Calculate the decimal - value of $\frac{\pi}{2}$

$\frac{\pi}{2}\approx\frac{3.14159}{2}=1.571$

Step3: Compare the two values

Since $0.556 < 1.571$, $\frac{5}{9}<\frac{\pi}{2}$. A right - angle in radians is $\frac{\pi}{2}$ radians.

Answer:

A. The angle is smaller than a right angle because $\frac{5}{9}$ is approximately $0.556$, which is less than $\frac{\pi}{2}\approx1.571$.