Triangle B C D is shown. Angle C D B is a right angle. Altitude a is drawn from point D to point E on side C B, forming a right angle. B D is labeled c and C D is labeled D. The length of B E is 18 and the length of E C is 4. What is the value of a?

6 StartRoot 2 EndRoot
9
8 StartRoot 3 EndRoot
36 StartRoot 2 EndRoot

6√2

6 StartRoot 2 EndRoot

Step-by-step explanation:

To solve for q, we apply the leg rule theorem or leg geometric mean theorem :

The hypotenus = 18 + 4 = 22

Leg 1 = b

Part1 = 4

According to the leg rule theorem :

Hypotenus / leg 1 = leg 1 / part 1

22 / b = b / 4

Cross multiply :

b * b = 22 * 4

b² = 88

b = √88 = √88 = √4 * √22 = 2√22

From Pythagoras :

a² = b² - 4²

a² = (√88)² - 16

a² = 88 - 16

a² = 72

a = √72 = √36 * √2 = 6√2

c. 6tan80

step-by-step explanation: