Question

In the figure, ABC and CDE are right-angled triangle in which angle ABC = 90,° angle CDE = 90, angle ACB = theta , angle ECD = Φ A B is 4 m and ED= 3 m if sin theta = 5/13 and cos .Φ
3/5 . Find the length of
of BD.​

Answer 1

Step-by-step explanation:

since in triangle ABC

sine theta =5/13=perpendicular/hypotnious

i,e AB/Ac=5/13

4/AC= 5/13

AC=10.4

Now in triangle EDC

COS phi= Base/hypotnious

CD/CE = 3/5

CD=(3/5)CE

By Pythagoras theorem

CE=

\sqrt{22.5}

22.5

there fore CD = (3/5)√22.5= 2.84

therefore BD= BC+CD

BD=10.4+2.84

BD= 13.25