Find the missing side of the right triangle. Round your answer to the nearest tenth. 38 units and 9 units

Answer 1

To find the missing side of a right triangle when two sides are known, we can use the Pythagorean theorem, which states:

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

where \(c\) is the length of the hypotenuse (the longest side), and \(a\) and \(b\) are the lengths of the other two sides.

From the information provided, it looks like 38 units and 9 units are the lengths of two sides. We need to determine whether 38 units is the hypotenuse or one of the other sides.

1. If 38 units is the hypotenuse: \[ a = 9 \] \[ c = 38 \] We can find side \(b\): \[ 9^2 + b^2 = 38^2 \] \[ 81 + b^2 = 1444 \] \[ b^2 = 1444 - 81 \] \[ b^2 = 1363 \] \[ b = \sqrt{1363} \approx 36.9 \text{ (to the nearest tenth)} \]

2. If 9 units is the hypotenuse, that cannot be, as it’s shorter than 38 units.

Therefore, the missing side of the right triangle is approximately 36.9 units when rounding to the nearest tenth.

Answer 2

44 and 10

Answer 3

To find the missing side of a right triangle with the given sides of 44 units and 10 units, we will again use the Pythagorean theorem:

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

where \(c\) is the hypotenuse.

Let’s consider two cases:

1. If 44 is the hypotenuse: Here, \(c = 44\) and one of the other sides \(a = 10\). We need to find \(b\):

   \[ 10^2 + b^2 = 44^2 \] \[ 100 + b^2 = 1936 \] \[ b^2 = 1936 - 100 \] \[ b^2 = 1836 \] \[ b = \sqrt{1836} \approx 42.9 \text{ (rounding to the nearest tenth)} \]

2. If 10 is the hypotenuse: This case is not possible as 10 is shorter than 44, meaning it cannot be the hypotenuse.

Thus, the missing side of the right triangle is approximately 42.9 units when rounding to the nearest tenth.

Answer 4

Wrong answer.

Answer 5

Let’s reevaluate the problem.

You have a right triangle with two sides given: 44 units and 10 units. We need to determine if we can apply the Pythagorean theorem correctly to find the missing side.

Scenario 1: 44 is the hypotenuse

If 44 is the hypotenuse (\(c\)) and 10 is one of the legs (\(a\)), we can find the other leg (\(b\)):

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

Substituting the values:

\[ 10^2 + b^2 = 44^2 \] \[ 100 + b^2 = 1936 \] \[ b^2 = 1936 - 100 \] \[ b^2 = 1836 \] \[ b = \sqrt{1836} \approx 42.9 \]

Scenario 2: 10 is the hypotenuse

If 10 is the hypotenuse, that scenario is not valid because it cannot be longer than the other side (44), making this case impossible.

Based on our evaluation, if the sides were indeed 44 and 10, with 44 as the hypotenuse, the calculation indicating the missing leg would still be approximately 42.9 units.

If you have specific criteria or corrections needed, please specify so I can provide an accurate response.

Answer 6

David wants to find the height of a building. He places his 44 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 10 feet. How tall is the building? Round your answer to the nearest tenth.

Answer 7

To determine the height of the building, we can use the Pythagorean theorem. In this scenario, the ladder acts as the hypotenuse of a right triangle, where:

• The height of the building is one leg (\(h\)).
• The distance from the base of the building to the foot of the ladder is the other leg, which is 10 feet.
• The length of the ladder is the hypotenuse, which is 44 feet.

Using the Pythagorean theorem:

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

where:

• \(a = h\) (the height of the building),
• \(b = 10\) feet (the base distance),
• \(c = 44\) feet (the length of the ladder).

Plugging in the values:

\[ h^2 + 10^2 = 44^2 \] \[ h^2 + 100 = 1936 \] \[ h^2 = 1936 - 100 \] \[ h^2 = 1836 \] \[ h = \sqrt{1836} \approx 42.9 \]

Thus, the height of the building is approximately 42.9 feet when rounded to the nearest tenth.

Answer 8

It is actually 42.8

Answer 9

Let’s go through the calculations step-by-step one more time to ensure accuracy.

Using the Pythagorean theorem:

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

Where:

• \(c\) is the hypotenuse (the ladder), which is 44 feet,
• \(b\) is the base distance from the building to the foot of the ladder, which is 10 feet,
• \(a\) is the height of the building (which we want to find).

Substituting the values into the equation:

\[ h^2 + 10^2 = 44^2 \]

Calculating the squares:

\[ h^2 + 100 = 1936 \]

Now, isolate \(h^2\):

\[ h^2 = 1936 - 100 \] \[ h^2 = 1836 \]

Now we calculate the square root of 1836:

\[ h = \sqrt{1836} \approx 42.8 \]

So you are correct: the height of the building is approximately 42.8 feet when rounded to the nearest tenth. Thank you for your patience, and I apologize for the error in my previous message!