If a right triangle has legs that are both 12 cm long, how long is the hypotenuse? Round the answer to the nearest hundredth.(1 point)

Question

Responses

17.0
17.0

288
288

16.97
16.97

Not enough information is given to solve the problem.

Answer 1

In a right triangle, you can find the length of the hypotenuse using the Pythagorean theorem, which states:

\[ c = \sqrt{a^2 + b^2} \]

where \(c\) is the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.

In this case, both legs are 12 cm long:

\[ c = \sqrt{12^2 + 12^2} \] \[ c = \sqrt{144 + 144} \] \[ c = \sqrt{288} \] \[ c \approx 16.97 \]

So, the length of the hypotenuse is approximately 16.97 cm when rounded to the nearest hundredth.

The correct answer is 16.97.

Answer 2

Sylvia is replacing a piece of siding on her house. To make the 12 ft. ladder stable, the bottom of the ladder needs to be 6 ft. from the base of her house. Applying the Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding

Answer 3

To find out how high the ladder will reach, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle:

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

In this scenario:

• \(c\) is the length of the ladder, which is 12 ft.
• \(b\) is the distance from the wall to the base of the ladder, which is 6 ft.
• \(a\) is the height the ladder reaches on the wall, which we want to find.

Plugging the known values into the Pythagorean Theorem:

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

Calculating the squares:

\[ 144 = 36 + a^2 \]

Now, isolate \(a^2\):

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

Now, take the square root of both sides to find \(a\):

\[ a = \sqrt{108} \] \[ a \approx 10.39 \]

Finally, rounding to the nearest tenth:

\[ a \approx 10.4 \]

So, the ladder will reach approximately 10.4 ft.

Answer 4

An electric pole has a support cable that is attached to the pole 20 ft. from the ground. The cable is anchored on the ground 10 ft. from the base of the pole. How long is the cable? Round to the nearest tenth

Answer 5

To find the length of the support cable, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

In this scenario:

• One leg of the triangle is the height at which the cable is attached to the pole, which is 20 ft.
• The other leg of the triangle is the distance from the base of the pole to the point where the cable is anchored on the ground, which is 10 ft.
• The length of the cable is the hypotenuse we want to find.

Using the Pythagorean theorem:

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

In our case:

• \(a = 20\) ft (height of the pole)
• \(b = 10\) ft (distance from the base of the pole)

Now, we can plug in these values:

\[ c^2 = 20^2 + 10^2 \]

Calculating the squares:

\[ c^2 = 400 + 100 \] \[ c^2 = 500 \]

Now, take the square root of both sides to find \(c\):

\[ c = \sqrt{500} \] \[ c \approx 22.36 \]

Finally, rounding to the nearest tenth:

\[ c \approx 22.4 \]

So, the length of the cable is approximately 22.4 ft.

Answer 6

A streetlight post needs some extra support for potential bad weather and high winds. The city wants to install metal support brackets on the light post. Each bracket will be braced into the ground and will then attach to a point on the pole that is 4.5 ft. from the ground. Each bracket is 6.5 ft. long. How far from the base of the pole should each bracket be braced in the ground? Round to the nearest tenth

Answer 7

To find out how far from the base of the pole the bracket should be anchored in the ground, we can apply the Pythagorean theorem. In this scenario:

• The length of each bracket (which acts as the hypotenuse of the right triangle) is \(c = 6.5\) ft.
• The height at which the bracket attaches to the pole (one leg of the triangle) is \(a = 4.5\) ft.
• The distance from the base of the pole to where the bracket is anchored in the ground will be the other leg of the triangle, denoted as \(b\).

According to the Pythagorean theorem:

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

Plugging in the known values:

\[ 6.5^2 = 4.5^2 + b^2 \]

Calculating the squares:

\[ 42.25 = 20.25 + b^2 \]

Now, isolate \(b^2\):

\[ b^2 = 42.25 - 20.25 \] \[ b^2 = 22 \]

Now, take the square root of both sides to find \(b\):

\[ b = \sqrt{22} \] \[ b \approx 4.690 \]

Finally, rounding to the nearest tenth:

\[ b \approx 4.7 \]

Therefore, each bracket should be braced into the ground approximately 4.7 ft from the base of the pole.