If a triangle has sides measuring 60, 75, and 45, is it a right triangle?(1 point)

Question

Responses

No, because 5,625 does not equal 3,600.
No, because 5,625 does not equal 3,600.

Yes, because 3,600 equals 3,600.
Yes, because 3,600 equals 3,600.

Yes, because 5,625 equals 5,625.
Yes, because 5,625 equals 5,625.

No, because 9,225 does not equal 2,025.

Answer 1

To determine if a triangle with sides measuring 60, 75, and 45 is a right triangle, we can use the Pythagorean theorem. A right triangle satisfies the condition \( c^2 = a^2 + b^2 \), where \( c \) is the longest side.

Here, the sides are:

• \( a = 45 \)
• \( b = 60 \)
• \( c = 75 \) (the longest side)

Now we calculate \( c^2 \) and \( a^2 + b^2 \):

• \( c^2 = 75^2 = 5625 \)
• \( a^2 + b^2 = 45^2 + 60^2 = 2025 + 3600 = 5625 \)

Since \( c^2 = a^2 + b^2 \) (i.e., \( 5625 = 5625 \)), the triangle is indeed a right triangle.

The correct response is: Yes, because 5,625 equals 5,625.

Answer 2

If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0

Answer 3

To determine if triangle DEF with sides measuring 50, 40, and 32 is a right triangle, we can use the Pythagorean theorem. The longest side is taken as the hypotenuse.

Here, the sides are:

• \( a = 32 \)
• \( b = 40 \)
• \( c = 50 \) (the longest side)

Now we check if \( c^2 = a^2 + b^2 \):

• \( c^2 = 50^2 = 2500 \)
• \( a^2 + b^2 = 32^2 + 40^2 = 1024 + 1600 = 2624 \)

Since \( 2500 \) does not equal \( 2624 \), triangle DEF is not a right triangle.

Therefore, the answer is 0.

Answer 4

If a right triangle has a leg with length 12 and the hypotenuse is 16, how long is the other leg? Round to the nearest tenth, if necessary

Answer 5

To find the length of the other leg in a right triangle, we can use the Pythagorean theorem, which states:

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

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

In this case:

• Let \( a = 12 \) (one leg)
• Let \( c = 16 \) (the hypotenuse)
• Let \( b \) be the length of the other leg, which we want to find.

Substituting the known values into the Pythagorean theorem:

\[ 16^2 = 12^2 + b^2 \]

Calculating the squares:

\[ 256 = 144 + b^2 \]

Now, subtract \( 144 \) from both sides:

\[ 256 - 144 = b^2 \]

\[ 112 = b^2 \]

Now, take the square root of both sides:

\[ b = \sqrt{112} \]

Calculating \( \sqrt{112} \):

\[ b \approx 10.583 \]

Rounding to the nearest tenth:

\[ b \approx 10.6 \]

Therefore, the length of the other leg is approximately 10.6.

Answer 6

Find the slant height of the square pyramid.
the height is 15 and the base is 16

Answer 7

To find the slant height of a square pyramid, we can use the following formula:

\[ l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2} \]

where:

• \( l \) is the slant height,
• \( h \) is the vertical height of the pyramid, and
• \( b \) is the length of the base (one side of the square base).

In this case:

• The height \( h = 15 \)
• The base \( b = 16 \)

First, we calculate \( \frac{b}{2} \):

\[ \frac{b}{2} = \frac{16}{2} = 8 \]

Now we substitute the values into the slant height formula:

\[ l = \sqrt{15^2 + 8^2} \]

Calculating the squares:

\[ l = \sqrt{225 + 64} \] \[ l = \sqrt{289} \]

Now, take the square root:

\[ l = 17 \]

Thus, the slant height of the square pyramid is 17.