Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2017-11-09 11:03:10

sydbernard
Member
Registered: 2017-09-04
Posts: 6

Angle measure question

1. Compute the angle at C of the triangle ABC if the altitudes at A and B intersect each other at an angle measuring 60◦. Consider all possibilities.
2. Compute the angle at C of the triangle ABC if the internal angle bisectors at A and B intersect each other at an angle measuring 60◦. Consider all possibilities.

So for 1 I think there is only 1 possibility in that the angle at C is 60 but are there actually more possibilities?

For 2 I think there are two possibilities depending on where the 60 is but I can't seem to figure out what the angle at C should be.

Offline

#2 2017-11-09 20:32:22

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,152

Re: Angle measure question

hi sydbernard

(1) I think it's only one as well.  If the altitudes are AD and BE and they meet at G, then DGB = 60 and GDB = 90 implies DBG = 30.

BEC = 90 and CBE = 30 implies BCE (BCA) = 60.

(2) Work in progress.

Later edit:  I am unable to draw a diagram for this at all.  Let D be where the bisectors cross.

A + B < 180  implies DAB + DBA < 90.  Therefore ADB > 90

Do you have a diagram?

Other post: I'm working on a method involving ellipses and circles.  If successful I'll post on that thread later.  Later edit: Done in other thread.

Bob

Last edited by bob bundy (2017-11-10 01:13:07)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

Board footer

Powered by FluxBB