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)

1 answer

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.