Answer:
2345
Step-by-step explanation:
The perimeter is the sum of all sides of the triangle.
Let us find the sides of the given triangle;
Using sine rule:
[tex]\frac{Sin A}{a}[/tex] = [tex]\frac{Sin B}{b}[/tex] = [tex]\frac{Sin C}{c}[/tex]
To find angle A;
90 + B + A = 180
90 + 27 + A = 180
A = 180 - 117 = 63°
A = 63°
B = 27°
[tex]\frac{Sin A}{a}[/tex] = [tex]\frac{Sin C}{c}[/tex]
A = 63°
a = ?
C = 90°
c = 1000
[tex]\frac{Sin 63}{a}[/tex] = [tex]\frac{Sin90}{1000}[/tex]
a = 1000Sin63 = 891
[tex]\frac{Sin B}{b}[/tex] = [tex]\frac{Sin C}{c}[/tex]
B = 27
[tex]\frac{Sin27}{b}[/tex] = [tex]\frac{Sin90}{1000}[/tex]
b = 1000Sin27 = 454
The perimeter of the triangle = a + b + 1000
= 891 + 454 + 1000
=2345
