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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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 (2017-11-10 01:13:07)

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