A brick layer is hired to build three walls

1. To the nearest degree, find the measure of angle A.

Assoli18 [71]

Answer:

(1) Option A is correct , The measure of angle A = 26°

(2) Option D is correct, The measure of angle B =70°

Step-by-step explanation:

(1)

In a right angle triangle figure-1 ,

* Hypotenuse(H) is always opposite the right angle and it is always the longest side of the triangle.

* Adjacent side (B) is the non-hypotenuse side that is next to a given angle A.

* Opposite side(P) is across from a given angle A.

To find the Angle A we use the Cosine ratio:

Cosine ratio states that the ratio of the adjacent side of a right triangle to the hypotenuse.

By definition of cosine ratio we have;

$\cos A = \frac{B}{H}$ ....[1]

In the figure - 1 we have B = 18 in and H = 20 in

substitute these in [1] to find angle A

$\cos A =\frac{18}{20} =\frac{9}{10} = 0.9$

or

$A = cos^{-1} (0.9)$

⇒ $A \approx 26^{\circ}$

therefore, the measure of angle A is, $26^{\circ}$

(2)P

In figure -2

Find the measure of angle B.

First find the side BC, using Pythagoras theorem;

Pythagoras theorem states that in the right angle triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Apply Pythagoras theorem in rt. angle ABC;

$AB^2 = AC^2+BC^2$

Substitute the values of AB = 5.1 cm and AC =4.8 cm to solve for BC

$(5.1)^2=(4.8)^2 +BC^2$

$26.01 = 23.04+BC^2$

Simplify:

$BC^2 = 2.97$ or

$BC = \sqrt{2.97} =1.723 cm$

Now, find the angle B, using tangent ratio;

Tangent ratio states that the ratio of the Opposite side of a right triangle to the adjacent side.

$\tan B = \frac{AC}{BC} =\frac{4.8}{1.732} =2.772$

$B = \tan^{-1} (2.772) \approx 70^{\circ}$

Therefore, the measure of angle B is; $70^{\circ}$ .

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0.5 to the fourth power equals 0.0625.

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The answer is d. m=f - a

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Which system of equations is consistent and dependent?

MAXImum [283]

Answer:

Step-by-step explanation:

4x − y = −11

2x + 3y = 5

lets multiply the second equation by -2 and add it to the first:

4x − y = −11

-4x - 6y = -10

------------------

0 - 7y = -21

y = -21/-7

y = 3

now we substitute this result in the first equation to find x:

4x − y = −11

4x - 3 = -11

4x = -8

x = -8/4

x = 2

so the solution is y = 3 and x =2

4x − 9y = −21

−10y = −30

we solve for y

−10y = −30

y = -30/-10

y = 3

and substitute in the first equation:

4x − 9y = −21

4x − 9(3) = −21

4x - 27 = -21

4x = 6

x = 6/4 = 3/2

so the solution is x = 3/2 and y = 3

4x + 3y = 5

2y = −6

we solve for y:

2y = −6

y = -6/2

y = -3

we do substitute in the first equation:

4x + 3y = 5

4x + 3(-3) = 5

4x - 9 = 5

4x = 14

x = 14/4

x = 7/2

so the solution is x = 7/2 and y = -3

7x − 3y = −11

9x = −6

we solve for x:

9x = −6

x = -6/9

x = -2/3

then we substitute in the first equation the result found:

7x − 3y = −11

7(-2/3) − 3y = −11

-14/3 - 3y = -11

we multiply by 3 to eliminate fractions:

-14 - 9y = -33

9y = 19

y = 19/9

so the solution is x = -2/3 and y = 19/9

12x − 3y = −33

14x = −28

we solve for x:

14x = −28

x = -28/14

x = -2

then we substitute in the first equation:

12x − 3y = −33

12(-2) − 3y = −33

-24 - 3y = -33

3y = 9

y = 3

then the solution is x = -2 and y = 3

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bulgar [2K]

Answer:

using pythagoras theorem

hyp 2=opp 2+adj 2

=( √6)(√6)+(√7)(√7)

hyp 2=13

hyp=√13

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