Question

in the triangle figure, side ab is 11, angle at b is 74 degrees, angle at c is a right angle, and we need to find the length of side bc (marked as x).

Explanation:

Step1: Identify adjacent side, hypotenuse

In right triangle \(ABC\), angle at \(B\) is \(74^\circ\), hypotenuse \(AB = 11\), side \(x\) is adjacent to \(74^\circ\). Use cosine function:
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute values and solve for \(x\)

Substitute \(\theta = 74^\circ\), hypotenuse \(=11\):
$x = 11 \times \cos(74^\circ)$
Calculate \(\cos(74^\circ) \approx 0.2756\):
$x \approx 11 \times 0.2756$

Answer:

$x \approx 3.03$