Identifying Trig Ratios (No Diagram) Score: \( 0 / 5 \quad \) Penalty: 1 off Question In \( \triangle \mathrm{BCD} \), the measure of \( \angle \mathrm{D}=90^{\circ}, \mathrm{DC}=28, \mathrm{CB}=53 \), and \( \mathrm{BD}=45 \). What ratio represents the cosine of \( \angle \mathrm{B} \) ?

To find the cosine of \( \angle \mathrm{B} \) in triangle \( \mathrm{BCD} \), we use the cosine ratio, which is defined as the adjacent side over the hypotenuse in a right triangle. For \( \angle \mathrm{B} \), the adjacent side is \( \mathrm{DC} = 28 \), and the hypotenuse is \( \mathrm{CB} = 53 \). Therefore, the cosine of \( \angle \mathrm{B} \) is given by: \[ \cos(\angle B) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{DC}{CB} = \frac{28}{53}. \] Real-world applications of trigonometry, particularly cosine ratios, are abundant! For example, engineers often rely on trig ratios when designing structures to ensure they have the right angles and lengths for stability. Cosine can help determine the height of a building or the length of a roof slope, making it a fundamental tool in architecture and construction projects. One common mistake when identifying trig ratios is confusing the sides relative to the angle. It’s essential to remember the relationships: in right triangles, the hypotenuse is always opposite the right angle, while the adjacent side is the one next to the angle in question. Make sure to visualize or even sketch the triangle to avoid mislabeling the sides, ensuring you use the correct lengths in your calculations!