A right triangle and two of its side lengths are shown in the diagram. Which measurement is closest to the value of x in feet?

Question

Image reference
A.
190.80 ft

B.
13.81 ft

C.
17 ft

D.
14.77 ft

Answer 1

To solve for \( x \) in a right triangle with given side lengths, we can use the Pythagorean theorem, which states:

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

where \( c \) is the hypotenuse and \( a \) and \( b \) are the other two sides.

Without knowing the specific lengths provided in your diagram, let's assume the following are the side lengths:

• Let \( a \) be one side.
• Let \( b \) be the other side.
• Let \( c \) be the hypotenuse.

If you have the lengths of any two of the sides, you can use the Pythagorean theorem to solve for \( x \) (which I assume corresponds to one of the sides).

For instance, if one side is 10 ft and the other side is \( x \) and the hypotenuse is 12 ft, we can set it up as:

\[ 10^2 + x^2 = 12^2 \] \[ 100 + x^2 = 144 \] \[ x^2 = 144 - 100 \] \[ x^2 = 44 \] \[ x = \sqrt{44} \approx 6.63 , \text{ft} \]

After you find the value of \( x \), you can compare it to the answer choices provided (A, B, C, D) to find the closest match.

If you provide the specific side lengths from the diagram, I can help calculate \( x \) based on that information.

Answer 2

1 is 3.7 ft and 14.3 ft and last is x

Answer 3

Given that one side of the right triangle is \( 3.7 \) ft, the other side is \( 14.3 \) ft, and we need to find the hypotenuse \( x \), we can use the Pythagorean theorem:

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

Here, let:

• \( a = 3.7 \) ft
• \( b = 14.3 \) ft
• \( c = x \) (the hypotenuse)

Now plug in the values:

\[ (3.7)^2 + (14.3)^2 = x^2 \]

Calculating the squares:

\[ 3.7^2 = 13.69 \] \[ 14.3^2 = 204.49 \]

Now add them together:

\[ 13.69 + 204.49 = x^2 \] \[ 218.18 = x^2 \]

Now take the square root to find \( x \):

\[ x = \sqrt{218.18} \approx 14.77 \text{ ft} \]

Among the choices provided:

A. 190.80 ft
B. 13.81 ft
C. 17 ft
D. 14.77 ft

The closest measurement to the value of \( x \) is D. 14.77 ft.

Answer 4

Sammi walked from her house to school and then to her friend’s house. The diagram shows the locations of these three places and their distances from each other. Which measurement is closest to the shortest distance in miles from Sammi’s house to her friend’s house?
Image reference
A.
0.6 mi

B.
1 mi

C.
0.45 mi

D.
0.2 mi

Answer 5

To find the shortest distance from Sammi’s house to her friend’s house, we can either use the Pythagorean theorem if the locations form a right triangle, or we may need to simply sum the direct paths if they follow a straight line or specific route.

Since I don't have access to the diagram you're referring to, I'll outline how to approach it:

1. Identify the Distances:

   • Find the distance Sammi walks from her house to school (let's call this distance \( A \)).
   • Find the distance from school to her friend’s house (let's call this distance \( B \)).

2. Applying the Pythagorean Theorem (if the path forms a right triangle):

   • If the path can be represented as a right triangle, use the formula: \[ d = \sqrt{A^2 + B^2} \]
   • Here, \( A \) and \( B \) are the two legs of the triangle.

3. Direct Path Calculation (straight-line distance):

   • If direct distances from her house to her friend's house are given, simply sum or compare the paths.

4. Choose the Closest Measurement: After calculating the distance, compare it to the options given:

   • A. 0.6 mi
   • B. 1 mi
   • C. 0.45 mi
   • D. 0.2 mi

Since I cannot see the actual diagram, could you provide the specific distances or more details about the paths? With that information, I can help you calculate and check against the options to find the answer.

Answer 6

0.4 and 0.2

Answer 7

Given that Sammi walks from her house to school for a distance of \( 0.4 \) miles and then from school to her friend's house for a distance of \( 0.2 \) miles, we need to determine the shortest distance from her house directly to her friend's house.

Steps to Calculate the Shortest Distance

1. Visualize the Path:

   • If you imagine Sammi's journey forms a right triangle with:
     • One leg equal to \( 0.4 \) miles (from her house to school).
     • The other leg equal to \( 0.2 \) miles (from school to her friend’s house).

2. Apply the Pythagorean Theorem:

   • The shortest distance (\( d \)) between Sammi's house and her friend's house can be calculated using: \[ d = \sqrt{(0.4)^2 + (0.2)^2} \]

3. Calculate:

   • Calculate \( (0.4)^2 \): \[ (0.4)^2 = 0.16 \]
   • Calculate \( (0.2)^2 \): \[ (0.2)^2 = 0.04 \]
   • Add the results: \[ 0.16 + 0.04 = 0.20 \]
   • Take the square root: \[ d = \sqrt{0.20} \approx 0.447 \text{ miles} \]

4. Compare with Given Choices:

   • A. 0.6 mi
   • B. 1 mi
   • C. 0.45 mi
   • D. 0.2 mi

Based on the calculation, the shortest distance from Sammi’s house to her friend’s house is approximately \( 0.447 \) miles, which is closest to C. 0.45 mi.

Answer 8

A window washer places a 12-foot ladder 6 feet away from a house as shown in the diagram. About how high is the window from the ground?
Image reference
A.
10.39 ft

B.
18 ft

C.
13.42 ft

D.
6 ft

Answer 9

To determine how high the window is from the ground based on the information given, we can use the Pythagorean theorem. The scenario can be illustrated as a right triangle:

• The ladder represents the hypotenuse of the triangle, which is 12 feet.
• One leg of the triangle represents the distance from the base of the ladder to the wall of the house, which is 6 feet (this is the base).
• The other leg represents the height of the window from the ground, which we will denote as \( h \).

According to the Pythagorean theorem:

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

Where:

• \( a \) is one leg (the distance from the wall, 6 feet),
• \( b \) is the other leg (the height of the window, \( h \)),
• \( c \) is the hypotenuse (the length of the ladder, 12 feet).

Plugging in the values:

\[ 6^2 + h^2 = 12^2 \]

Calculating the squares:

\[ 36 + h^2 = 144 \]

Now, isolate \( h^2 \):

\[ h^2 = 144 - 36 \] \[ h^2 = 108 \]

Taking the square root to find \( h \):

\[ h = \sqrt{108} \approx 10.39 , \text{ft} \]

Therefore, the height of the window from the ground is approximately 10.39 ft.

The answer is A. 10.39 ft.