in triangle abc angle B equal to 90 degree and AB:AC = 24 : 25 . If BC equals to 14 find the perimeter of triangle ABC
Answers
Answer:
112
Step-by-step explanation:
abc is right angled triangle
24:25 = 48 : 50
14^ + 48 ^ = 50^
196+2304=2500
2500=2500
thus sides of triangle 14,48 and 50
perimeter = 50+48+14 = 112
Given:
Angle B = 90°
AB:AC = 24:25
Length of BC = 14
To find:
Find the perimeter of the triangle ABC.
Solution:
It is given the triangle is a right-angled triangle with a right angle at B.
Therefore AB: AC will be equal to cos A.
cos A = 24/25
cos A = 0.96
angle A = 16.26°
Now we will find the angle C using the angle sum property of the triangle.
A + B + C = 180°
C = 180 - ( 90 + 16.26)
C = 73.73°
Now we will find BC using cos C
cos C = BC/AC
cos C = 14/x
0.28 = 14/x
x = 50
therefore AC = 50
Now AB/AC = 24/25
AB = 0.96 x 50
AB = 48
Therefore perimeter of the triangle = AB + BC + AC
= 14 + 50 + 48
= 112 units
Therefore the perimeter of the triangle ABC will be 112 units.