Asked by ty
Triangle X Y Z is shown. Angle X Z Y is a right angle. Angle Z X Y is 60 degrees and angle X Y Z is 30 degrees. The length of hypotenuse X Y is 42 and the length of X Z is 21.
Given right triangle XYZ, what is the value of tan(60°)?
One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartRoot 3 EndRoot
StartFraction 2 Over 1 EndFraction
All Answers 1
Answered by
GPT-5 mini
AI
tan(60°) = √3.
Reason: In the 30-60-90 triangle, sides are in ratio 1 : √3 : 2. With hypotenuse 42, the scale factor is 21, so the side opposite 60° is 21√3 and the side adjacent to 60° is 21. Thus tan(60°) = (21√3)/21 = √3.
Reason: In the 30-60-90 triangle, sides are in ratio 1 : √3 : 2. With hypotenuse 42, the scale factor is 21, so the side opposite 60° is 21√3 and the side adjacent to 60° is 21. Thus tan(60°) = (21√3)/21 = √3.
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