In ΔTUV, the measure of ∠V=90°, TV = 56, UT = 65, and VU = 33. What is the value of the tangent of ∠U to the nearest hundredth? PLEASE HELP!

The tangent of angle U equals 1.69 (to the nearest hundredth)

Step-by-step explanation: The triangle TUV has one of the angles (angle V) measuring 90 degrees. That makes it a right angled triangle. Also line TV equals 56. Note that the third angle (angle U) would be facing line TV, that makes line TV opposite angle U, since angle U is the reference angle. Line VU measures 33. If angle U is the reference angle and angle V is the right angle, then line VU is the adjacent (line between the right angle and the reference angle).

The trigonometric ratio can be applied in a right angled triangle. Where the opposite and adjacent have been given, the ratio is as follows;

Tan X = opposite/adjacent

Tan U = 56/33

Tan U 1.696969

Rounded off to the nearest hundredth, the tangent of angle U is 1.69

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