Answer:
The answer is C. 10.0 cm.
Step-by-step Explanation:
Since triangles ACD and ABE are similar, the angles within each of them are the same:
This implies that the sine of the angle at A = opposite ÷ hypotenuse (for triangle ACD) = opposite ÷ hypotenuse (for triangle ABE).
Opposite for triangle ACD = 15 cm
Hypotenuse for triangle ACD = 12 + 6 = 18 cm
Opposite for triangle ABE = x
Hypotenuse for triangle ABE = 12 cm
Therefore, 15/18 = x/12
or x = (15 × 12) ÷ 18
x = 10 cm.
