In triangle BED, tan theta = 4.  Find BE.  Give an exact answer.

To answer this question, we need more information about triangle BED. The value of tan theta = 4 gives us the ratio of the opposite side to the adjacent side in a right triangle, but without knowing the length of either the opposite side (BD) or the adjacent side (DE), or the angle theta, we cannot determine the length of BE.

If this is a right triangle and theta is the angle at E, then we could use the Pythagorean theorem to find BE if we knew either BD or DE. For example, if BD = 4 and theta = 45 degrees, then DE = BD/tan(theta) = 4/4 = 1 and BE = sqrt(BD^2 + DE^2) = sqrt(4^2 + 1^2) = sqrt(17).

But without additional information, we cannot find BE.

To answer this question, we need more information about triangle BED. The value of tan theta = 4 gives us the ratio of the opposite side to the adjacent side in a right triangle, but without knowing the length of either the opposite side (BD) or the adjacent side (DE), or the angle theta, we cannot determine the length of BE.

If this is a right triangle and theta is the angle at E, then we could use the Pythagorean theorem to find BE if we knew either BD or DE. For example, if BD = 4 and theta = 45 degrees, then DE = BD/tan(theta) = 4/4 = 1 and BE = sqrt(BD^2 + DE^2) = sqrt(4^2 + 1^2) = sqrt(17).

But without additional information, we cannot find BE.