Question

Use trig to find a side. Solve for x. Round to the nearest tenth, if necessary. HG number is x. IH number is 96. What is the number for IK. The angle for this triangle is 22.

Answer 1

I need one clarification: which vertex is the 22° angle at, and which side is IH (the 96) relative to that angle — is IH the side opposite the 22° angle, the side adjacent to it, or the hypotenuse? Also, is the triangle right-angled?

Below are the common possibilities and the corresponding IK values (rounded to one decimal). Let θ = 22°.

1) If IH = 96 is the side adjacent to θ and IK is the side opposite:
IK = 96 * tan(22°) = 96(0.4040) ≈ 38.8

2) If IH = 96 is the side adjacent to θ and IK is the hypotenuse:
IK = 96 / cos(22°) = 96 / 0.9272 ≈ 103.5

3) If IH = 96 is the hypotenuse and IK is the adjacent side:
IK = 96 * cos(22°) = 96(0.9272) ≈ 89.0

4) If IH = 96 is the hypotenuse and IK is the opposite side:
IK = 96 * sin(22°) = 96(0.3746) ≈ 36.0

5) If IH = 96 is the side opposite θ and IK is the adjacent side:
IK = 96 / tan(22°) = 96 / 0.4040 ≈ 237.7

6) If IH = 96 is the side opposite θ and IK is the hypotenuse:
IK = 96 / sin(22°) = 96 / 0.3746 ≈ 256.4

Tell me which case matches your diagram (or upload the diagram), and I’ll give the single correct value.