Question

In triangle abc, m of acb = 90, cd is perpendicular to ab , m of acd is 60. and bd is 5 cm. find ad

Answer 1

ITS 9

Explanation:

Answer 2

Let us draw a picture to make the things more clear.

Attached is the image.

We have been given that

`\angle acd = 60 ^(\circ)`

Therefore, we have

`\angle dcb =90- 60= 30 ^(\circ)`

Now, in triangle bcd, we have

`\tan30 = (5)/(cd)\\ \\ (1)/(\sqrt 3)=(5)/(cd)\\ \\ cd=5\sqrt 3`

Now, in triangle acb, we have

`tan 60 = (ad)/(5\sqrt3) \\ \\ \sqrt 3=  (ad)/(5\sqrt3)\\ \\ ad= 5\sqrt3 * \sqrt 3\\ \\ ad= 5* 3\\ \\ ad=15`

Thus, ad is 15 cm.