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Maru [420]
3 years ago
9

A triangle has side lengths of 10, 11, and 15 . what type of triangle is it?

Mathematics
1 answer:
Trava [24]3 years ago
7 0
Answer: scalene and obtuse

Justification:

You can find the angles using the law of cosine:

c^2 = a^2 + b^2 - 2abcos(γ)

=> cos(γ) = [a^2 + b^2 - c^2] / (2ab)

1) cos(γ) = [10^2 + 11^2 - 15^2] / (2*10*11) = - 0.0181818

=> γ = arccos(-0.0181818} ≈ 91°

2) cos(α) = [b^2 + c^2 - a^2 ] / 2bc = [11^2 + 15^2 - 10^2] / (2*11*15] = 0.7454545

=> α = arccos(0.7454545) ≈ 41.8°

3) cos(β) = [a^2 + c^2 - b^2] / (2ac) = [10^2 + 15^2 - 11^2] /(2*10*15) = 0.68

=> β = arccos(0.68) ≈ 47.2°

4) Verification: 91° + 41.8° + 47.2° = 180°

5) The triangles with the three different sides are called scalenes (which you can tell with only the measures of the sides).

6) The triangles with one angle greater than 90° are called obtuse.

So, the triangle is scalene and obtuse.
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3 years ago
Find the surface area of a triangular prism that has the following dimensions. Use the formula SA = 2B + Ph.
OverLord2011 [107]
Answer: The surface area of the triangular prism is 448 square millimeters.

To find the surface area, we just need to input our values into the formula that is given.

SA = 2B + Ph
SA = 2(84) + 56(5)
SA = 168 + 280
SA = 448

The final surface area is 448 mm^2.
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3 years ago
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7. The volume, V, of any cube with a side length, s, can be determined using the formula V = S^3 (s x s x s). What is the volume
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count the blocks or use brain

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What is the least common denominator (LCD) of 12 and 23?
leva [86]

Answer: none of those, 276...?

Step-by-step explanation:

You need to know the least common denominator (LCD) of 12 and 23 if you want to add or subtract two fractions with 12 and 23 as denominators.

The least common denominator, also called lowest common denominator (LCD), of 12 and 23 is 276.

Here is a math problem example where you need to know the LCD of 12 and 23 to solve:

3/12 + 2/23 = ?

Step 1) Take the LCD and divide each denominator by it as follows:

276/12 = 23

276/23 = 12

Step 2) Multiply each nominator with the respective answers from Step 1:

3 x 23 = 69

2 x 12 = 24

Step 3) Put it all together to solve the problem:

69/276 + 24/276 = 93/276

= 3/12 + 2/23 = 93/276

It's that easy! Once again, the lowest common denominator (LCD) of 12 and 23 is as follows:

276

7 0
3 years ago
-2x+y=-12, 3y- 2x=-12
inessss [21]

Answer:

x = 6

y = 0

Explanation:

−2x+y=−12;3y−2x=−12

Rewrite equations:

−2x+y=−12;−2x+3y=−12

Solve −2x+y=−12 for y

−2x+y=−12

−2x+y+2x=−12+2x(Add 2x to both sides)

y=2x−12

Substitute 2x−12 for y in −2x+3y=−12

−2x+3y=−12

−2x+3(2x−12)=−12

4x−36=−12 (Simplify both sides of the equation)

4x−36+36=−12+36 (Add 36 to both sides)

4x=24

Divide both sides by 4

4x / 4 = 24 / 4

x = 6

Substitute 6 for x in y=2x−12

y=2x−12

y=(2)(6)−12

y=0 (Simplify both sides of the equation)

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3 years ago
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