Question

what is the length of $overline{ac}$? round to the nearest tenth.
a triangle with right angle at c, angle at a is 55 degrees, side bc is 15 m.
options: 10.5 m, 12.3 m, 18.3 m, 21.4 m

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \(ABC\) with \(\angle C = 90^\circ\), \(\angle A = 55^\circ\), and \(BC = 15\) m. We can use the tangent function, where \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\tan(55^\circ)=\frac{BC}{AC}\), so we can solve for \(AC\) as \(AC=\frac{BC}{\tan(55^\circ)}\).

Step2: Substitute the values

We know \(BC = 15\) m and \(\tan(55^\circ)\approx1.4281\). So \(AC=\frac{15}{\tan(55^\circ)}=\frac{15}{1.4281}\approx10.5\) m.

Answer:

10.5 m