Answer:
The ratio representing the tangent of T is 7 : 24.
Step-by-step explanation:
Consider the right angles triangle STU below.
In the triangle STU, the angle U is 90°.
The measure of the sides are as as follows:
Perpendicular = SU = 7 units
Base = UT = 24 units
Hypotenuse = TS = 25 units.
According to the Pythagorean theorem,
Hypotenuse² = Perpendicular² + Base²
Check if the above measurements satisfies the theorem or not.
Hypotenuse² = Perpendicular² + Base²
(25)² = (24)² + (7)²
625 = 576 + 49
625 = 625
Thus, the measurements are correct.
Now according to the trigonometric identities for a right angles triangle, the tangent of an angle is:
[tex]tan\ \theta=\frac{Perpendicular}{Base}[/tex]
Compute the tangent of angle T as follows:
[tex]tan\ \text{T}=\frac{SU}{UT}[/tex]
[tex]tan\ \text{T}=\frac{7}{24}[/tex]
Thus, the ratio representing the tangent of T is 7 : 24.
