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3 years ago

13POINTS!!!

Mathematics

1 answer:

prohojiy [21]3 years ago

7 0

Answer:

When we know all 3 sides we use the law of cosines

a = 47

b = 11

c = 38

cos (A) = (b^2+c^2-a^2) / (2bc)

cos (A) = -0.7703349282

Angle A = 140.38

cos (B) = (a^2 + c^2 -b^2) / (2ac)

cos (B) = 0.9888017917

Angle B = 8.5826 degrees

cos (C) = (a^2 + b^2 -c^2) / 2ab

cos (C) = 0.8568665377

cos (C) = 31.033 degrees

Angle W would be the smallest angle so it equals

31.033 degrees or rounded to nearest tenth

31.03

Step-by-step explanation:

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Find the distance from point A(−14, 5) to the line −x+2y = 14.

Ad libitum [116K]

Answer:

The distance from point A to given line is: 2√5 or 4.472 units

Step-by-step explanation:

Given equation of line is:

$-x+2y= 14$

And the point is:

$A = (x_1,y_1) = (-14,5)$

The standard form of equation of line is:

$Ax+By+C = 0$

Converting the given equation into standard form

$-x+2y-14=0$

The distance of a point (x1,y1) from a line is given by the formula:

$d = \frac{|Ax_1+By_1+C}{\sqrt{A^2+B^2}}$

In the given details,

A = -1, B = 2, C = -14

x1 = -14, y1 = 5

Putting the values in the formula

$d = \frac{|(-1)(-14)+(2)(5)-14|}{\sqrt{(-1)^2+(2)^2}}\\d = \frac{14+10-14}{\sqrt{1+4}}\\d = \frac{10}{\sqrt{5}}\\d = \frac{5*2}{\sqrt{5}}\\d = \frac{\sqrt{5}*\sqrt{5}*2}{\sqrt{5}}\\d = 2\sqrt{5}\\d = 4.472\ units$

Hence,

The distance from point A to given line is: 2√5 or 4.472 units

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