Question

In triangle ABC, if angle ACB is 90° and CB is perpendicular to AD, and angle ACD is 30°, and AD is 6 cm, find BD.

Answer 1

To find BD, we can use the concept of trigonometry. Since angle ACB is 90° and angle ACD is 30°, we can use the trigonometric ratios of a right triangle to calculate the length of BD. BD ≈ 3.464 cm.

Step-by-step explanation:

To find BD, we can use the concept of trigonometry. Since angle ACB is 90° and angle ACD is 30°, we can use the trigonometric ratios of a right triangle to calculate the length of BD.

AD is the adjacent side to angle ACD and BD is the opposite side. The tangent ratio is defined as the opposite side divided by the adjacent side. Therefore, we have:

tan(30°) = BD/AD

tan(30°) = BD/6

BD = 6 * tan(30°)

BD = 6 * 0.5774

BD ≈ 3.464 cm