Math Is Fun Forum

SolarDevil

Member

Registered: 2014-09-14

Posts: 37

Trig Problem

is a regular tetrahedron (right triangular pyramid).  If M is the midpoint of

, then what is

?

Last edited by SolarDevil (2014-11-03 12:00:23)

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SolarDevil

Member

Registered: 2014-09-14

Posts: 37

Re: Trig Problem

Nevermind I got that one!
However could I have help on another one?

In right triangle

, we have

and D is the midpoint of

.  If AB = 7 and BC = 25, then what is

?

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Herro! Sycamore School will win National Science Bowl this year!!!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Trig Problem

hi SolarDevil,

Let each side be length s.

All the faces are equilateral triangles so you should be able to calculate AM and BM, in terms of s.

Then, in the triangle ABM, you know all the sides in terms of s.

Use the cosine rule to get the angle.  (You can cancel the s.)

EDIT: I was preparing my post when you posted.  I'll look at the new one and make another post.

Bob

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Trig Problem

Similar approach.  Use Pythagoras to get AC, hence DC and DA.

Use Pythagoras again to get BD.

Now you know all the sides in BDC so the cosine rule will give you the angle.

EDIT: As you want the tangent you can save time by getting tan BDA.  Then tan BDC is the obtuse angle from this.

Bob

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

SolarDevil

Member

Registered: 2014-09-14

Posts: 37

Re: Trig Problem

Okay. Thanks so much!

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Herro! Sycamore School will win National Science Bowl this year!!!