In ijk, i=170 inches, j=119 and k=42.find the area of ijk, to the nearest square inch

9514 1404 393

  25,975 in²

Step-by-step explanation:

Since your j+k < i, we assume that not all of these dimensions are side lengths. If we assume ...

  i = 170 in

  J = 119°

  K = 42°

Then we can find side j using the law of sines.

  I = 180° -119° -42° = 19°

Then the law of sines tells us ...

  j/sin(J) = i/sin(I)

  j = i·sin(J)/sin(I) = (170 in)sin(119°)/sin(19°) = 456.695

Then the area of the triangle is ...

  A = (1/2)(i·j·sin(K)) = (1/2)(170 in)(456.695 in)sin(42°) ≈ 25,975.03 in²

The area of triangle IJK is about 25,975 square inches.