Triangles are formed by the intersection of the lines y=x, y 2x, y=-2x, and y=-4. solve for angles abc and abd a d b

Answer and Step-by-step explanation:

To find the angles between the lines, we can use the formula:

tanα = |ms - mr| / | 1 + ms.mr|

where ms and mr are the linear coefficients of the lines you want to find. It always finds the smaller angle formed.

Let's find all the angles from the triangles formed.

y=x     ms = 1

y=2x   mr = 2

tanα = |1 - 2| / | 1 + 1.2|

tanα = |-1| / | 1 + 2|

tanα = |-1/3|

tanα = 1/3

α = tan⁻¹1/3

α = 18.4°

y=x     ms = 1

y=-4   mr = 0

tanα = |1 - 0| / | 1 + 1.0|

tanα = |1| / | 1 + 0|

tanα = |1/1|

tanα = 1

α = tan⁻¹1

α = 45°

y=2x     ms = 2

y=-4     mr = 0

tanα = |2 - 0| / | 1 + 2.0|

tanα = |2| / | 1 + 0|

tanα = |2/1|

tanα = 2

α = tan⁻¹2

α = 63.4°

As these 2 lines are in both triangles, the suplement of this angle is also asked, so, 180° - 63.4° = 116.6°

For y=2x and y=-4, it's the same: α = 63.4°  

y=2x     ms = 2

y=-2x     mr = -2

tanα = |2 - (-2)| / | 1 + 2.(-2)|

tanα = |4| / | 1 - 4|

tanα = |4/3|

tanα = 4/3

α = tan⁻¹ 4/3

α = 53.1°

what is the question?

step-by-step explanation:

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}