Question

Given: △АВС, m∠ACB = 90° CD ⊥ AB , m∠ACD = 30°, AC = 8 cm Find: BD

Answer 1

To find the length of BD in triangle ABC, use the trigonometric ratio tangent to find CD, and then subtract CD from AB.

Step-by-step explanation:

In triangle ABC, CD is perpendicular to AB, AC = 8 cm, and angle ACD = 30 degrees. We need to find the length of BD.

To solve this problem, we can use trigonometry. Since triangle ACB is a right triangle with angle ACB = 90 degrees, we can use the trigonometric ratio tangent to find the length of BD.

Tan(ACB) = opposite / adjacent = CD / AB

Since angle ACD = 30 degrees and angle ACB = 90 degrees, we can find angle ABC = 60 degrees (angle sum property of triangles).

Tan(60) = CD / AB = sqrt(3) / 1

Since AB = AC = 8 cm, we can substitute the values and solve for CD.

sqrt(3) = CD / 8

CD = 8 * sqrt(3)

Now, to find BD, we can subtract CD from AB.

BD = AB - CD = 8 - 8 * sqrt(3)