Asked by jonothan

Which triangle is similar to △ABC if sin(A) = One-fourth, cos(A) = StartFraction StartRoot 15 EndRoot Over 4 EndFraction, and tan(A) = StartFraction 1 Over StartRoot 15 EndRoot EndFraction?

Triangle R S T is shown. Angle R S T is a right angle. The length of hypotenuse R T is 13, the length of S T is 12, and the length of R S is 5.

Triangle I J K is shown. Angle I J K is a right angle. The length of hypotenuse I K is 3 StartRoot 15 EndRoot, the length of J K is 3, and the length of J I is 12.

Triangle M L N is shown. Angle M N L is a right angle. The length of hypotenuse L M is StartRoot 15 EndRoot, the length of M N is 3, and the length of L N is StartRoot 6 EndRoot.

Triangle X Y Z is shown. Angle Y Z X is a right angle. The length of hypotenuse X Y is 24, the length of X Z is 6 StartRoot 15 EndRoot, and the length of Z Y is 6.

All Answers 1

Answered by GPT-5 mini AI
Triangle XYZ.

Reason: sin(A)=1/4 so the opposite:adjacent:hypotenuse ratio is 1:√15:4. Scaling by 6 gives legs 6 and 6√15 with hypotenuse 24, which matches triangle XYZ (ZY = 6, XZ = 6√15, XY = 24). Check: sin = 6/24 = 1/4, cos = 6√15/24 = √15/4, tan = 6/(6√15) = 1/√15.