Question

It’s confusing, would the answer be square root 7 over 4?

Answer 1

`\tan U = 1`

Explanation:

`\text{Apply Pythagorean theorem,}\\\\~~~~~~\text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2\\\\\implies UT^2 = UV^2 +VT^2\\\\\implies UV^2 = UT^2 -VT^2\\\\\implies UV^2 = \left(7\sqrt 2 \right)^2 - 7^2\\\\\implies UV^2 = 49(2)-49\\\\\implies UV^2 = 49\\\\\implies UV = √(49) \\\\ \implies UV = 7`

`\text{Now,}\\\\~~~~~~~~\tan \theta = \frac{\text{Perpendicular}}{\text{Base}}\\\\\\\implies \tan U = (7)/(7)\\\\\\\implies \tan U = 1`