Question

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

∠L
∠L

WT¯¯¯¯¯¯¯¯¯
line segment cap w cap t

LT¯¯¯¯¯¯¯
line segment cap l 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)

Answer 1

To determine the hypotenuse of the triangle, we need to identify the sides. In a right triangle, the hypotenuse is the side opposite the right angle, which is the longest side of the triangle.

If we have a triangle with vertices \( W \), \( L \), and \( T \):

- \( WT \) (line segment WT) connects points \( W \) and \( T \).
- \( LT \) (line segment LT) connects points \( L \) and \( T \).
- \( WL \) (line segment WL) connects points \( W \) and \( L \).

Assuming that angle \( L \) is the right angle, the hypotenuse of the triangle would be the side opposite to that angle, which is \( WT \).

So, the hypotenuse of the triangle is **\( WT \)**.

---

Now, to find the length of \( TL \) when \( WT = 53 \) and \( LW = 45 \), we can apply the Pythagorean theorem, which states:

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

where \( c \) is the hypotenuse (in this case, \( WT \)), and \( a \) and \( b \) are the other two sides (\( LW \) and \( TL \)).

Given
- \( WT = c = 53 \)
- \( LW = a = 45 \)
- \( TL = b \) (unknown)

We can set up the equation:

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

Calculating \( 45^2 \) and \( 53^2 \):

\[
2025 + TL^2 = 2809
\]

Next, we will isolate \( TL^2 \):

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

Finally, taking the square root of both sides to find \( TL \):

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

Thus, the length of \( TL \) is **28**.