Question

The angle measures in a triangle are in the ratio 1:3:5. The longest side of the triangle measures 5 inches. What is the approximate perimeter of the triangle?

Answer 1

Answer:

C

Step-by-step explanation:

Answer 2

X + 3x + 5x = 180
9x = 180
x = 20
So the angles are
20
60 and
100

Let's say longest side is c, its length is 5 and it is opposite angle C.

Using the Law of Sines: http://www.1728.org/trigtut2.htm

c / sin(C) = b / sin (B)
5 / sin (100) = b / sin (60)
5 * sin (60) / sin(100) = side b
5 * 0.86603 / 0.98481 = side b
4.33015 / 0.98481 = side b
side b = 4.3969395112

Using the Law of Sines Again:
c / sin(C) = a / sin (A)
5 / sin (100) = a / sin (20)
5 / 0.98481 = a / 0.39073
5 * 0.34202 / 0.98481 = side a
1.7101  / .98481 = side a
side a =  1.736477087

SO, perimeter =
5  (side c) plus
4.3969395112 (side b) plus
1.736477087 (side a)


11.1334165982 TOTAL