Answer to Question #92734 in Trigonometry for mahdi

Question

Describe any pattern or trend you can see in the values of angles A, B, and V as you move closer to or further away from the wall.

Answer 1

Solution.

Firstly, we need to consider the case of measuring the angle between the straight line, which is applied to the corresponding segment (the person who stands in front of the wall) and the plane (the wall). Presuming that the person stands straight, we are supposed to claim that the straight line is parallel to the plane. As long as it is true, the angle between the straight line and the plane equals zero.

Once we've considered this case of condition, let us examine another alternative: solve the problem establishing a parallel relationship between the segment VB and the straight that belongs to plane of the wall(let this straight bed called 'w').

(1) The distance between the segment and the straight line is the perpendicular distance any point on one line to the other line. So, let OV be the distance between the segment VB and the straight line w.

Consequently,$\angle{V}=90\degree$ and $\angle{A}=90\degree-\angle{B}$ ((2)the result of values of two acute angles in the right triangle)

$\sin\angle{A}=\frac{h}{l}$ . As long as $\sin\angle{A}$ is inversely proportional to $l$ , an increase in $l$ gives a decrease in $\sin\angle{A}$ .

$\angle{A}\isin(0,90).$According to this, $y=\sin\angle{A} \uparrow$ (increases). If $\sin\angle{A} \uparrow$ , $l\downarrow$ (decreases). As a consequence of that, if $l\uparrow$, $\angle{A} \downarrow$. Conclusion: the further we go away from the wall, the less the value of $\angle{A}$ is.

$B=90\degree-\angle{A}$ . Because of this, the decrease of $\angle{A}$ gives an increase of $\angle{B}$. Conclusion: the further we move, the more the value of $\angle{B}$ is.

In the case we considered $\angle{V}=90\degree$ is constant.

Answer: the value of $\angle{A}$ increases with moving closer to the wall;the value of$\angle{B}$ increases with moving further away from it.if $\angle{V}$ is a constant.