Question 1

Which is the hypotenuse of the triangle?(1 point)
Responses

LT¯¯¯¯¯¯¯
line segment cap l cap t

∠L
∠L

WT¯¯¯¯¯¯¯¯¯
line segment cap w cap t

WL¯¯¯¯¯¯¯¯¯
line segment cap w liters
Question 2
If WT = 53 and LW = 45, find TL. You must show all work in order to earn full credit for the problem, including your original equation. You may either type your answer or upload a picture. (3 points)

1 answer

To identify the hypotenuse of the triangle, let's first analyze the triangle's sides based on standard definitions in a right triangle. The hypotenuse is the longest side, opposite the right angle.

In your case, without an explicit triangle configuration or diagram, the line segments mentioned are:

  1. LT
  2. WT
  3. WL

If we assume this is a right triangle with W at the right angle, then WT can be identified as the hypotenuse, as well as the longest side of the triangle.

Question 1:

The hypotenuse of the triangle is WT.


Question 2:

Given:

  • WT = 53 (hypotenuse)
  • LW = 45

We need to find TL. We can use the Pythagorean theorem, which states:

\[ a^2 + b^2 = c^2 \]

Where:

  • \(c\) is the length of the hypotenuse (WT),
  • \(a\) and \(b\) are the lengths of the other two sides (LW and TL).

In this scenario, we can position the segments as follows:

  • \(LW\) is one leg of the triangle,
  • \(TL\) is the other leg of the triangle,
  • \(WT\) is the hypotenuse.

Using the values, the equation becomes:

\[ LW^2 + TL^2 = WT^2 \]

Substituting the known values into the equation:

\[ 45^2 + TL^2 = 53^2 \]

Calculating the squares:

\[ 2025 + TL^2 = 2809 \]

Now, isolate \(TL^2\):

\[ TL^2 = 2809 - 2025 \] \[ TL^2 = 784 \]

Now, take the square root of both sides:

\[ TL = \sqrt{784} \] \[ TL = 28 \]

Final Answer for Question 2:

The length TL is 28.