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lesya692 [45]
3 years ago
8

In triangle abc angle a = 40◦, side b = 11 and side c = 5. use the cosine rule to find the length of side a, to two decimal plac

es. without using the cosine rule again, find the remaining angles b and c, giving your answers to the nearest degree.
Mathematics
1 answer:
Sonbull [250]3 years ago
5 0
A^2 = b^2 + c^2 - 2bc cos a

    = 11^2 + 5^2 - 2*5*11 cos 40

   =  7.86 to 2 DP's

to find the remaining angles use the sine rule:-
a / sin A = b / sin B so

7.857/ sin 40 =  11 / sin B
sin B = 11 sin40 / 7.857 = 0.8999

<B = 64 degrees 

so <C = 180 - 64-40  =  76 degrees
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According to the Rational Root Theorem, which is not a possible solution of the
trapecia [35]

Answer:

  5/2

Step-by-step explanation:

Possible rational roots are ...

  ±(divisor of 9)/(divisor of 2)

So, the possibilities are ...

  ±1/2, ±1, ±3/2, ±3, ±9/2, ±9

The one on your list that is not among these is 5/2.

5/2 is not a possible rational root.

8 0
3 years ago
Find the length x It would help me so much thanks
sergij07 [2.7K]

Answer:

x = 7

Step-by-step explanation:

\frac{x}{6}  =  \frac{3.5}{3}

3x = 21

x = 7

7 0
3 years ago
(17 PTS)<br> GEOMETRY QUESTIONS, PLEASE HELP!
nekit [7.7K]
14. 
Angles 4 and 6 are supplementary, because they are on the same line. Supplementary angles add up to 180 degrees, and a line must be 180 degrees.

15.
Angles 1 and 8 are congruent, because they are alternate exterior angles

16.
m = y2 - y1 / x2 - x1
m = 7 - 2 / 4 - 5
m = 5 / -1
m = -5

17.
m = 3 - 3 / 7 - (-5)
m = 0 / 12
m = 0

18.
m = 1 - (-2) / 5 - (-4)
m = 3 / 9
m = 1/3

19.
A = (0, 3) - B = (3,0)
m = 0 - 3 / 3 - 0
m = -3 / 3
<em>m = -1</em>
C = (0, -2) - D = (4, 2)
m = 2 - (-2) / 4 - 0
m = 4 / 4
<em>m = 1</em>
Perpendicular, because the slopes are opposite reciprocals.

20.
E = (1, 2) - F = (0, 0)
m = 0 - 2 / 0 - 1
m = -2 / -1
<em>m = 2</em>
G = (1, -3) - H = (3, 0) 
m = 0 - (-3) / 3 - 1
<em>m = 3 / 2</em>
Neither, because the slopes are different.

21.
I = (0, 1) - J = (2, -4)
m = -4 - 1 / 2 - 0
<em>m = -5/2</em>
K = (-1, -2) - L = (4, 0)
m = 0 - (-2) / 4 - (-1)
<em>m = 2/5</em>
Perpendicular, because the slopes are opposite reciprocals.

22.
M = (-2, 2) - N = (2, 2)
Horizontal line
<em>m = 0</em>
O = (3, 0) - P = (-3, 0)
Horizontal line
<em>m = 0
</em>Parallel, because the slopes are the same.
<em>
</em>23.
Angle 2 is congruent to angle 1 because of the alternate exterior angle theorem.
Angle 1 is congruent to angle 3 because of the vertical angle theorem.
Angle 2 is congruent to angle 3 because of substitution.
Line l is parallel to line m because the corresponding angles are congruent.
7 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=8x%20-%206%20%2B%2011x%20%2B%202%20%2B%203x%20-%205" id="TexFormula1" title="8x - 6 + 11x + 2
ollegr [7]

8x - 6 + 2 + 3x - 5
Combine like terms
11x - 9
This is the answer
6 0
3 years ago
-4^2-17
Irina18 [472]

Answer:

Step-by-step explanation:

-4 is really  -1 * 4

-4² = -1 * 4²

-4² = -1 * 16

-4² = -16

Use parenthesis  to square

(-1 * 4)² = (-4)²

(-4)² = 16

5 0
3 years ago
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