Triangle XYZ is rotated 90° counterclockwise about the origin. On a coordinate plane, triangle X Y Z has points (1, 3), (4, nega
2 answers:
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Answer: option C
Step-by-step explanation:
The diagram of the triangle is shown in the attached photo. The triangle is a right angle triangle ABC
Assuming the given angle is #,
Recalling the trigonometric ratio,
tan # = opposite / adjacent
If tan # = 4, it means
opposite / adjacent = 4/1
Therefore, opposite = 4 and adjacent = 1
Applying Pythagoras theorem,
Hypotenuse^2 = opposite ^2 + adjacent ^2
Hypotenuse = AC
Opposite = 4
Adjacent = 1
AC^2 = 4^2 + 1^2 = 17
AC = ± √17
To determine cos #, we would apply another trigonometric ratio,
Cos# = adjacent /hypotenuse
Cos# = 1/±√17
Cos # =-1 /√17 or 1/√17
