Question

In a triangle abc.Am is perpendicular on bc. If tan b =3/4, tan c =5/12 and bc is 56 cm, find the length of am

Answer 1

Please refer to the attachment.. AM = 15cm

Answer 2

Answer: 15 cm

Step-by-step explanation:

Here, in triangle ABC,  AM is a perpendicular on the segment BC,

Thus, $tan B = \frac{AM}{BM}$

$\frac{3}{4}=\frac{AM}{BM}$ ( Given tan B = 3/4 )

Let, AM= 3x and BM = 4x

Where x is any number,

Now,

$tanC = \frac{AM}{MC}$

$\implies \frac{5}{12}=\frac{AM}{MC}$    ( Given tan C = 5/12 )

Let, AM = 5y and MC = 12y

Where y is any number,

⇒ 3x = 5y

⇒ x = 5/3 y

Again,Given  BC = 56

⇒ BM + MC = 56

⇒ 4x + 12y = 56

⇒ x + 3y = 14

⇒ $\frac{5}{3}y+3y = 14$

⇒ $\frac{5y+9y}{3}=14$

⇒ $\frac{14y}{3}=14$

⇒ y = 3

Hence, The length of AM = 5y = 5×3 = 15 cm.