Question

find bd.

(image of a right triangle bcd with right angle at b, bc = 6, angle at d is 45°)

write your answer in simplified, rationalized form. do not round.
bd =

Explanation:

Step1: Identify Triangle Type

Triangle \( BCD \) is right - angled at \( B \), and \( \angle D = 45^\circ \). So, \( \angle C=180^\circ - 90^\circ - 45^\circ = 45^\circ \). Thus, \( \triangle BCD \) is an isosceles right - triangle, where \( BC = BD \) (in an isosceles right - triangle, the legs are equal).

Step2: Determine Length of BD

We know that \( BC = 6 \). Since \( BC = BD \) (from the property of isosceles right - triangle), then \( BD = 6 \).

Answer:

\( 6 \)