Question

AM is perpendicular to BC . if tan B =3\4, tan C =5\12 and BC= 56, find the AM

Answer 1

Answer:

Step-by-step explanation:

With the help of the given information, a triangle is constructed.

Refer to the image attached.

We will use tan ∅  = Perpendicular /Base in the triangle to use as sides.

As you can see in the figure, the perpendicular and base sides corresponding to angle B are 3x and 4x and the perpendicular and base corresponding to angle C are 5y and 12y.

From the triangle, you can see that 3x = 5y, or x = 5y/3.----------equation 1

We can also see that 4x + 12y = 56, or x + 3y = 14-----------equation 2

Now, use equation 1 in equation 2,

that is , put x = 5y/3 in x+ 3y = 14

We get, 5y/3 + 3y = 14

or, 5y + 9y = 42

or, 14y = 42

or, y = 3

and hence x = 5

Now , we know that AM = 3x = 5y

Hence AM =  3(5) = 15 or AM = 5(3) =15

Hence, AM = 15.