Analyze the diagram below and complete the instructions that follow.

Mathematics

1 answer:

Sladkaya [172]2 years ago

8 0

The large triangle is isosceles, so that the two smaller triangles that appear inside the large one have bases of 12/2, or 6.

Let's see how x and y are related:

sin 60 degrees = opp/hyp = x/y = sqrt(3) / 2

and cos 60 degrees = adj/hyp = 1/2 = 6 / y. Then y = 12 (which should be no surprise, since the large triangle is equilateral).

Then: x/y = sqrt(3) / 2, or

x sqrt(3) x
---- = ----------- = ------ , so that 2x = 12sqrt(3), or x=6sqrt(3).
y 2 12

In summary,
x = 6√3
y=12

You might be interested in

Y = -3/4x - 2

oksian1 [2.3K]

Answer:

One Solution

Step-by-step explanation:

Trust me

4 0

2 years ago

Distance between parallel lines y=3x+10 and y=3x-20

Alecsey [184]

1. Take an arbitrary point that lies on the first line y=3x+10. Let x=0, then y=10 and point has coordinates (0,10).

2. Use formula $d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}$ to find the distance from point $(x_0,y_0)$ to the line Ax+By+C=0.

The second line has equation y=3x-20, that is 3x-y-20=0. By the previous formula the distance from the point (0,10) to the line 3x-y-20=0 is:

$d=\dfrac{|3\cdot 0-10-20|}{\sqrt{3^2+(-1)^2}}=\dfrac{30}{\sqrt{10}}=3\sqrt{10}$ .

3. Since lines y=3x+10 and y=3x-20 are parallel, then the distance between these lines are the same as the distance from an arbitrary point from the first line to the second line.

Answer: $d=3\sqrt{10}$ .