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Nastasia [14]
3 years ago
9

In triangle ABC, A is a right angle, and mB = 45°. Find BC. If your answer is not an integer, leave it in simplest radical form.

Mathematics
1 answer:
Nikolay [14]3 years ago
3 0

This triangle is called a 45-45-90 triangle, and the side ratio for the sides opposite to the 45-45-90 degree angles respectively are 1-1-sqrt2

Now we know one side is 6 and its opposing the 45 degrees angle and BC is opposing the 90 degrees angle the ratio between the sides are 1:sqrt2

Therefore BC=6*sqrt2=6sqrt2

Thus B is the correct answer!

Hope this helped any questions just leave them in the comments of this answer.

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Find the length of the radius of the circle, which is inscribed into a right trapezoid with lengths of bases a and b.
egoroff_w [7]

Answer:

  r = (ab)/(a+b)

Step-by-step explanation:

Consider the attached sketch. The diagram shows base b at the bottom and base a at the top. The height of the trapezoid must be twice the radius. The point where the slant side of the trapezoid is tangent to the inscribed circle divides that slant side into two parts: lengths (a-r) and (b-r). The sum of these lengths is the length of the slant side, which is the hypotenuse of a right triangle with one leg equal to 2r and the other leg equal to (b-a).

Using the Pythagorean theorem, we can write the relation ...

  ((a-r) +(b-r))^2 = (2r)^2 +(b -a)^2

  a^2 +2ab +b^2 -4r(a+b) +4r^2 = 4r^2 +b^2 -2ab +a^2

  -4r(a+b) = -4ab . . . . . . . . subtract common terms from both sides, also -2ab

  r = ab/(a+b) . . . . . . . . . divide by the coefficient of r

The radius of the inscribed circle in a right trapezoid is r = ab/(a+b).

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The graph in the second attachment shows a trapezoid with the radius calculated as above.

6 0
4 years ago
Which inequality is a true statement.
MArishka [77]

Answer:

c

Step-by-step explanation:

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7 0
3 years ago
Find the acute angle between the two given lines<br><br> y=-2x and y=x
Marina CMI [18]

Answer:

θ ≈ 71.6°

Step-by-step explanation:

The angle between two lines with slopes m₁ and m₂ is:

tan θ = | (m₂ − m₁) / (1 + m₁m₂) |

Here, m₁ = -2 and m₂ = 1.

tan θ = | (1 − (-2)) / (1 + (-2)(1)) |

tan θ = | 3 / -1 |

tan θ = 3

θ ≈ 71.6°

3 0
4 years ago
a sphere is circumscribed about an 8-inch by 8-inch by 8-inch cube. Find the volume to the nearest cubic inch.
Anit [1.1K]

The volume of the cube is (8 x 8 x 8)  =  8³  =  <em>512 cubic inches</em>  (exact)


7 0
4 years ago
Ashley is digging for rocks at a geological site. She has 140 meters of rope and 4 stakes to mark off a rectangular area. Which
yuradex [85]

Answer:

C

Step-by-step explanation:

Let's go through each set of dimensions and test them. Keep in mind that two times the sum of the length and width of a rectangle yields the perimeter.

A) 2(14+10)=2(24)=48

B) 2(70+70)=2(140)=280

C) 2(60+10)=2(70)=140

Therefore, the correct answer is C. Hope this helps!

8 0
3 years ago
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