Question

Determine the perimeter of the following triangle, to the nearest whole unit.

Answer 1

2345

Explanation:

The perimeter is the sum of all sides of the triangle.

Let us find the sides of the given triangle;

Using sine rule:

`(Sin A)/(a)` =
`(Sin B)/(b)` =
`(Sin C)/(c)`

To find angle A;

90 + B + A = 180

90 + 27 + A = 180

A = 180 - 117 = 63°

A = 63°

B = 27°

`(Sin A)/(a)` =
`(Sin C)/(c)`

A = 63°

a = ?

C = 90°

c = 1000

`(Sin 63)/(a)` =
`(Sin90)/(1000)`

a = 1000Sin63 = 891

`(Sin B)/(b)` =
`(Sin C)/(c)`

B = 27

`(Sin27)/(b)` =
`(Sin90)/(1000)`

b = 1000Sin27 = 454

The perimeter of the triangle = a + b + 1000

= 891 + 454 + 1000

=2345