We can see a right triangle in this problem,
where a vertical distance is a leg that opposite to the angle 20⁰ , and horizontal distance is an adjacent leg to the 20⁰ angle.
So,
tan (20⁰) = opposite leg/adjacent leg
tan (20⁰) = vertical distance/horizontal distance
tan (20⁰) = 30 /horizontal distance
horizontal distance= 30/tan(20⁰) ≈ 82.4 in.
y - y1 = m(x - x1) Point slope form
y - y1 = 4(x - x1) Plug in the given slope m = 4
y - (-10) = 4(x - 3) Plug in the given (x1,y1) point
y + 10 = 4(x - 3) Simplify
y + 10 = 4x - 12 Distribute
y+10-10 = 4x - 12 - 10 Subtract 10 from both sides
y = 4x - 22 Combine like terms
Answer is choice A
You are given two equations, solve for one variable in one of the equations. Say you solved for x in the second equation. Then, plug in that value of x in the x of the first equation. Solve this (first) equation for y (as it should become apparent) and you'll get a number value. Plug in this numerical value of y into the y of the second equation. Solve for x in the second equation. And there you have it: (x, y)