Question

find ( mangle b ).
write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle b=) 。

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(ABC\) with \(\angle C = 90^{\circ}\), we know the opposite side \(AC = 2\) and the adjacent side \(BC=1\) with respect to \(\angle B\). We use the tangent ratio: \(\tan B=\frac{\text{opposite}}{\text{adjacent}}\).
So, \(\tan B=\frac{AC}{BC}\).

Step2: Substitute the values

Substitute \(AC = 2\) and \(BC = 1\) into the tangent formula: \(\tan B=\frac{2}{1}=2\).

Step3: Find the angle

To find \(B\), we use the inverse tangent function. If \(\tan B = 2\), then \(B=\tan^{- 1}(2)\).
Using a calculator, \(B\approx63.4^{\circ}\).

Answer:

$63.4^{\circ}$