Question #b7272

Question

227 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-11T06:11:06

Area of the right triangle #A_t = color (red)(30)#

Length of Altitude #AD = color (red)(4.6155)#

enter image source here

Area of the triangle #A_t = (1/2) * (AB) * (AC) = (1/2) * c * b = (1/2) * 5 * 12 = color(red)(30)#

#a / sin A = b / sin B = c / sin C#

#13 / sin (pi/2) = 12 / sin B = 5 / sin C#

#sin B = (12/13) * sin (pi/2) = 0.9231#

In right triangle ABH,

Altitude #AH = c sin B = 5 * 0.9231 = color(red)(4.6155)#

Aliter:
Consider triangles BAH & BCA

Both are similar.

#:. (AH) / (CA) = (BA) / (BC)#

#AH = ((CA)*(BA)) / (BC) = (12*5) / 13#

#AH = 60 / 13 = color (red)(4.6155)#