In triangle RST, angle S is a right angle and cdc R=13/12. What is Tan T?

answers: 13/5, 12/13, 12/5, 5/12

csc R = 13/12 = 1/sin R

1/Sin R = 13/12
sin R = 12/13 = Y/r.

X^2 + Y^2 = r^2
X^2 + 12^2 = 13^2
X^2 = 13^2 - 12^2 = 25
X = 5.

Tan T = Y/X = 12/5

Well, let's take a look at triangle RST. Since angle S is a right angle, we can use some trigonometric ratios to help us out. Now, we know that the tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.

Considering angle T, the adjacent side is RS and the opposite side is RT. Unfortunately, we don't have the exact measurements of RS and RT. So, unless we have more information, we can't determine the value of Tan T.

But don't worry, the world of triangles is vast and full of other interesting facts. So feel free to ask about something else, and I'll be here to clown around and provide answers!

To find Tan T in triangle RST, we need to find the length of the opposite side (ST) and adjacent side (RT) to angle T.

Since angle S is a right angle, we can use the Pythagorean Theorem to find the length of ST. Let's say the length of ST is x:

ST^2 = RS^2 + RT^2

Since RS = RT - 13/12, we can substitute this value:

x^2 = (RT - 13/12)^2 + RT^2

Expanding and simplifying:

x^2 = RT^2 - (2 * 13/12 * RT) + (13/12)^2 + RT^2

x^2 = 2RT^2 - (2 * 13/12 * RT) + (13/12)^2

Since angle S is a right angle, RT is the hypotenuse, and we know that:

RT^2 = RS^2 + ST^2

Substituting the values, we have:

RT^2 = (RT - 13/12)^2 + x^2

Expanding and simplifying:

RT^2 = RT^2 - (2 * 13/12 * RT) + (13/12)^2 + x^2

Since RT^2 cancels out, we are left with:

0 = - (2 * 13/12 * RT) + (13/12)^2 + x^2

- (2 * 13/12 * RT) = (13/12)^2 + x^2

- (2 * 13/12 * RT) = 169/144 + x^2

Now, we know that Tan T is equal to the opposite side (ST) divided by the adjacent side (RT), so:

Tan T = ST / RT

Substituting the known values, we have:

Tan T = x / RT

From the above equation, we can solve for x by rearranging the equation for ST:

x = RT * Tan T

Substituting this value of x in the equation - (2 * 13/12 * RT) = 169/144 + x^2, we get:

- (2 * 13/12 * RT) = 169/144 + (RT * Tan T)^2

Since we are trying to find Tan T, we cannot solve this equation directly. We need more information about the lengths of the sides RT or RS. Without those values, we cannot determine the exact value of Tan T.

To find the value of Tan T in triangle RST, we need to use the given information about angle S and side RS.

Since angle S is a right angle, we know that it measures 90 degrees, which means that angle T is the remaining angle in the triangle.

We are given the length of side RS, which is denoted as cdc R, and its length is 13/12.

Now, to find Tan T, we need to determine the ratio of the length of the side opposite angle T (denoted as Opposite) to the length of the side adjacent to angle T (denoted as Adjacent).

In this case, Opposite is the length of side ST, and Adjacent is the length of side RT.

Since we are not given the lengths of these sides, we need to use the Pythagorean theorem to find them.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In our triangle RST, the hypotenuse is the side RS, so we can write the equation as follows:

RS^2 = ST^2 + RT^2

Substituting the values we know, we have:

(13/12)^2 = ST^2 + RT^2

Simplifying:

169/144 = ST^2 + RT^2

Now, we can't determine the exact lengths of ST and RT based on this equation alone, but we can determine their ratio.

Let's solve for ST^2:

ST^2 = (169/144) - RT^2

Next, we can substitute this value into the equation for Tan T:

Tan T = Opposite / Adjacent
= ST / RT

Substituting the value we found for ST^2:

Tan T = √[(169/144) - RT^2] / RT

Based on the answer choices provided, we can plug in the values of RT and check which one satisfies the equation.

For example, if we choose RT = 12, we can find the value of Tan T:

Tan T = √[(169/144) - 12^2] / 12

Evaluating this expression will give us the value of Tan T, which can then be compared with the answer choices provided.

Therefore, we need to determine the length of side RT to find the value of Tan T.