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Jobisdone [24]
3 years ago
14

Find b, given that a = 20, angle A = 30°, and angle B = 45° in triangle ABC

Mathematics
2 answers:
Kamila [148]3 years ago
6 0
<span>The side b is opposite to the angle B, applying the law of the sines, we have:

</span>\frac{a}{sinA} = \frac{b}{sinB}
\frac{20}{sin30^0} = \frac{b}{sin45^0}
\frac{20}{ \frac{1}{2} } = \frac{b}{ \frac{ \sqrt{2} }{2} }
20* \frac{ \sqrt{2} }{2}  = b* \frac{1}{2}
\frac{20 \sqrt{2} }{2} = \frac{b}{2}
2*b =2*20 \sqrt{2}
2b = 40 \sqrt{2}
b =  \frac{40 \sqrt{2} }{2}
\boxed{b = 20 \sqrt{2} }
Inga [223]3 years ago
4 0

Answer:

b = 20√2

Step-by-step explanation:

Given: ΔABC

           a = 20 , m∠A =  30° and m∠B = 45°

To find: value of b.

We use Sine result, which state that

\frac{a}{sin\,A}=\frac{b}{sin\,B}

Substituting given values we, get

\frac{20}{sin\,30^{\circ}}=\frac{b}{sin\,45^{\circ}}

we know that sin\,30^{\circ}=\frac{1}{2}\:and\:sin\,45^{\circ}=\frac{1}{\sqrt{2}}, we get

\frac{20}{\frac{1}{2}}=\frac{b}{\frac{1}{\sqrt{2}}}

20{\times2}=b\times\sqrt{2}

b\times\sqrt{2}=40

b=\frac{40}{\sqrt{2}}

b=20\sqrt{2}

Therefore, b = 20√2

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12. Find the surface area of each figure to the nearest tenth.
Zolol [24]

Answer:

  12a. 471.2 cm²

  12b. 60 m²

Step-by-step explanation:

Part A.

The surface area of each figure is the sum of the end area and the lateral area.

  <u>cylinder</u>

  S = (2)(πr²) +2πrh = 2πr(r +h)

  S = 2π(5 cm)(5 cm +10 cm) =150π cm² ≈ 471.2 cm²

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  <u>triangular prism</u>

  S = (2)(1/2)bh + PL . . . . b=triangle base; h=triangle height; P=triangle perimeter; L=length of prism

  S = (4 m)(1.5 m) + ((4 + 2·2.5) m)(6 m) = (6 + 54) m² = 60 m²

_____

Part B.

Surface area is useful in the real world wherever products are made from sheets of material or wherever coverings are applied.

Carpeting or other flooring, paint, wallpaper are all priced in terms of the area they cover, for example.

The amount of material used to make containers in the shapes shown will depend on the area of these containers (and any material required for seams).

6 0
2 years ago
Luis wants to buy a pair of jeans that costs $24. If the tax rate is
muminat

Answer:

25 68/100

Step-by-step explanation:

percent means 1/100th.

7 percent=7/100

24 times 7/100= 1 68/100

24+1 68/100=25 68/100

7 0
3 years ago
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 16 + 2x − x^2, [0, 5]
RSB [31]

Answer:

<h2>absolute maximum = 16</h2><h2>absolute minimum = 1</h2>

Step-by-step explanation:

To get the absolute maximum and minimum values of the function f(x) = 16 + 2x − x² n the given interval [0,5], we need to get the values of f(x) at the end points. The end points are 0 and 5.

at x = 0;

f(0) =  16 + 2(0) − 0²

f(0) = 16

at the other end point i.e at x = 5;

f(5) =  16 + 2(5) − 5²

f(5) = 16 + 10-25

f(5)= 26-25

f(5) = 1

The absolute minimum value is 1  and  occurs at x  = 5

The absolute maximum value is 16 and  occurs at x  = 0

5 0
3 years ago
BRAINLIEST ASAP!!!!
ivanzaharov [21]
The graph of a quadratic equation is a U-shaped curved called parabola. It is because the parabola makes very easy to find the axis of symmetry to plot selected points and finding the roots and vertex.

Good luck :)
4 0
3 years ago
Noah loves the Half-Tens facts and often uses them to solve multiplication problems. Make up a 2-digit by 3-digit multiplication
Stells [14]

Half Tens is a way of multiplying where we have to find the value of given numbers. First we double any 'one' of the two given numbers and multiply both to get an answer. Then we divide that answer by '2' to get the answer.

Lets take two numbers as 16 and 340

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Now we will divide this by 2

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So, if we check 16\times340=? , it is 5440.

Similarly if we double the number 340, we get 680

Now, 16\times680=10880

And 10880/2 = 5440

Hence, in both ways the answer is 5440.

6 0
3 years ago
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