Trig Tuesday

[kolyur]

Find the length of the dotted line.

I blew through it and got the wrong answer, then realized the complication. My second attempt was correct but took longer. NO CAD, and bonus points if you can do it without making any extra sketches.

 

[kamenges]

15.86.

I'm pretty sure I did this the hard way but first I figured out all the angles around the various triangles based on the lengths given. I then drew a line from where the line we are measuring meets the large triangle to the base of the large triangle. Based on that I defined two equations:

tan(11.3) = X/Y
tan(35)=X/(20-Y)

11.3 is the angle of the line we are measuring to the base
35 is the angle of the side of the large triangle to the base
X is the length of the line normal to the base of the large triangle to where the line we are measuring meets the right side of the large triangle
Y is the base of the right triangle formed by the line we are measuring and X

Solve one of the equations for one of the variables, substitute that solution into the correct spot in the other equation and away you go.

Keith

 

[L D[AR2P#0.0]]

Invalid geometric construction.

Slope of dotted line is 1/5

The slope of any line perpendicular to the dotted line is -5

Slope of line shown perpendicular to the dotted line is -7/10 hence it is not perpendicular.

 

[kamenges]

That threw me for a second too. It isn't drawn with the correct proportions so you can't trust the "look" of the drawing.

But, since only lengths are given and none of the length combinations violate any geometric constructs, the basic question is valid.

Keith

 

[L D[AR2P#0.0]]

Have you drawn this to scale?

 

[Steve Bailey]

I don't see where the dotted line is shown perpendicular to any line.

Define 0, 0 at the lower left corner of the triangle.

Equation of the dotted line: Y = 0.2X
Equation of the right side of the triangle: Y = -.7X + 14

Solve the two equations for X to get the X coordinate of the intersection:
X = 14/0.9 = 15.556

Solve the two equations for Y to get the Y coordinate of the intersection:
Y = 14/4.5 = 3.111

Length of the line from 0, 0 to 15.556, 3.111 is the square root of X^2 + Y^2

Length = 15.86

 

[L D[AR2P#0.0]]

Ah.... my bad, I've made the mistake of "seeing" a right angle when there isn't one

 

[JRoss]

Not invalid, just poorly drawn. There's nothing that claims the dotted line intersects the side of the triangle at 90 degrees.

EDIT: Ignore me, I'm just slow to post....

 

[kolyur]

Ah.... my bad, I've made the mistake of "seeing" a right angle when there isn't one

Exactly, that's what I did too. Obviously the drawing is way out of scale and that's the "trick." In order to solve it I had to re-sketch that part of the diagram with the angle closer to what it should be, so that I could project a true perpendicular line.

15.8 is the correct answer.