Answer:
j = 19.6
k = 25.9
J = 49°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.
Analysis
The given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...
Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin
Tan = Opposite/Adjacent ⇒ Adjacent = Opposite/Tan
Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.
Application
Hypotenuse = Opposite/Sin
IJ = 17/sin(41°) ≈ 25.9
Adjacent = Opposite/Tan
IK = 17/tan(41°) ≈ 19.6
Angle J = 90° -41° = 49°
In summary, ...
j = 19.6
k = 25.9
J = 49°
