Answer:
12.22
Explanation:
Since this is a right triangle, we solve using the trig. ratios. You remember then with the acronym SohCahToa.
It is read as:
Sine is opposite over hypotenuse.
Cosine is adjacent over hypotenuse.
Tangent is opposite over adjacent.
Which side is opposite or adjacent depends on which angle is the angle of reference, the angle you are talking about. The adjacent side touches the angle of reference.
If angle I is the angle of reference, side HI is the adjacent side.
Since we have information for the opposite side, GH, we can use the tangent ratio.
Substitute known information (tanI and GH) with specific values.
tanI = tan42° ≈ 0.90
= opposite/adjacent
= GH/HI
= 11/HI
0.90 = 11/HI
(HI)0.90 = 11 Rearrange equation
HI = 11/0.90 Divide both sides by 0.90 to isolate HI
HI = 12.22 Rounded to 2 decimal places
HI is measured for 12.22 units.