All categories

2 years ago

Solve the triangle.

Mathematics

1 answer:

vekshin12 years ago

8 0

9514 1404 393

Answer:

b = 757.7 m
A = 17.2°
C = 14.3°

Step-by-step explanation:

From the law of cosines, you can find the length of side b to be ...

b = √(a² +c² -2ac·cos(B))

b = √(184041 +128164 -307164cos(148.5°)) ≈ √574105.36

b ≈ 757.7

From the law of sines, you can find the measure of angle C to be ...

C = arcsin(c/b·sin(B))

C ≈ arcsin(358/757.7·sin(148.5°)) ≈ arcsin(0.246872)

C ≈ 14.3°

A = 180° -148.5° -14.3°

A = 17.2°

_____

Some graphing calculators have built-in triangle-solving functions. Apps are available for the purpose for phone or tablet. The screenshot shows a web site that does a nice job of solving the triangle.

You might be interested in

Check/correct my work please! Working with polynomials and stuff.

OLEGan [10]

1. (b+2)(b+2)=b^2 +4b + 4 (FOIL)
2. FOIL; x^2 + 6x + 9
3. correct

8 0

3 years ago

Pllllllllllllllllllllleasee one guys i neeed ur help one

Svetllana [295]

${ \qquad\qquad\huge\underline{{\sf Answer}}}$

Let's solve ~

Calculate discriminant :

$\qquad \sf \dashrightarrow \: 3 {x}^{2} + 6x - 1$

a = 3
b = 6
c = 1

$\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac$

$\qquad \sf \dashrightarrow \: d = (6) {}^{2} - (4 \times 3 \times 1)$

$\qquad \sf \dashrightarrow \: d = 36 - 12$

$\qquad \sf \dashrightarrow \: d = 24$

$\qquad \sf \dashrightarrow \: \sqrt {d} = 2 \sqrt{6}$

Now, let's calculate it's roots ( x - intercepts )

$\qquad \sf \dashrightarrow \: x = \cfrac{ - b \pm \sqrt{d} }{2a}$

$\qquad \sf \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{2 \times 3}$

$\qquad \sf \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{6}$

So, the intercepts are :

$\qquad \sf \dashrightarrow \: x = \cfrac{ - 6 - 2 \sqrt{6} }{6}$

and

$\qquad \sf \dashrightarrow \: x = \cfrac{ - 6 + 2 \sqrt{6} }{6}$

5 0

1 year ago

Read 2 more answers

Reference attached image for the problem.Please show your work for finding the partial area.

-Dominant- [34]

To find the area of a sector of a circle use the next formula:

$A=\frac{\theta}{360º}*\pi *r^2$

As the given circle has a outside angle 90º (it is not part of the sector of the circle) subtract the 90º from 360º (total angle of a circle) to find the angle of the sector:

$\theta=360º-90º=270º$

Find the area of the sector with angle 270º:

$\begin{gathered} A=\frac{270º}{360º}*3.14*(11in)\placeholder{⬚}^2 \\ \\ A=0.75*3.14*121in^2 \\ \\ A=284.955in^2 \end{gathered}$ Then, the approximate area of the given sector of a circle is 284.955 square inches

7 0

1 year ago

Find the trig ratio. Reduce to<br> lowest terms.

Vlad [161]

COS A=0.8

Step-by-step explanation:

2^6+8^2

100

sqrt(100)=10

8/10

0.8

6 0

3 years ago

Read 2 more answers

A rectangle length is 8cm more than three times it’s widith. The perimeter is 128 cm find the length.

Masteriza [31]

Let x = width
<span>length is 8 cm more than three times it’s width so length = 3x + 8
</span>
Perimeter of a rectangle = 2(L + W)
so
128 = 2(x + 3x + 8) solve for x (width)
128 = 2(4x + 8)
64 = 4x + 8
4x = 56
x = 14
width = 14 cm
length = 3(14) + 8 = 50 cm

Answer:
width = 14 cm
length = 50 cm

4 0

3 years ago