Question

find the distance from point c to point b. enter as a decimal rounded to the nearest tenth.
diagram: right triangle ( abc ) with right angle at ( b ), ( angle bac = 56^circ ), ( ab = 390 , \text{m} ), ( cb ) (horizontal leg) labeled ( cb = ? , \text{m} ), and a building illustration near ( b ).

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle \( ABC \) with \( \angle B = 90^\circ \), \( AB = 390 \) m, and \( \angle BAC = 56^\circ \). We need to find \( CB \). Using the tangent function, \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). Here, \( \theta = 56^\circ \), opposite side to \( \theta \) is \( CB \), and adjacent side is \( AB \). So, \( \tan(56^\circ)=\frac{CB}{AB} \).

Step2: Solve for \( CB \)

Substitute \( AB = 390 \) m into the formula: \( CB = AB\times\tan(56^\circ) \). Calculate \( \tan(56^\circ)\approx1.4826 \). Then \( CB = 390\times1.4826 \approx 578.2 \) (rounded to the nearest tenth).

Answer:

\( 578.2 \)