The angle of the triangle will be 20°, 60°, and 100°. Then the perimeter of the triangle will be 11.1 inches.
Let the triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c.
Then by the sine law, we have
[tex]\rm \dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b} = \dfrac{\sin\angle C}{c}[/tex]
The angle measures in a triangle are in the ratio 1:3:5.
Then the angle be x: 3x: 5x.
The sum is 180°.
x + 3x + 5x = 180°
9x = 180°
x = 20°
Then the angle of the triangle will be 20°, 60°, and 100°.
[tex]\rm \dfrac{\sin 20^o}{a} = \dfrac{\sin 60^o}{b} = \dfrac{\sin 100^o}{5}[/tex]
From last 2 terms, we have
sin 60° / b = sin 100° / 5
b = 4.4 inches
From first and last terms, we have
sin 20° / a = sin 100° / 5
a = 1.7
Then the perimeter of the triangle will be
P = 5 + 4.4 + 1.7
P = 11.1 inches
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