Math Is Fun Forum

DarkTangent

Member

Registered: 2017-07-03

Posts: 20

Trigonometry

1. In right triangle

, we have

and

is the midpoint of

. If

and

, then what is

?

2. If

is an acute angle such that

, then find

.

I have been working on these problems for quite a while. Please help! Thank you!

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All our dreams can come true if we have the courage to pursue them - Walt Disney

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Trigonometry

hi DarkTangent

1.)  If you draw a line from D to BC parallel to AB, the point where this line crosses BC , say E, will be the midpoint of BC and ED will be half BA.

Use Pythag to calculate AC, work out DC and then tan BDC = ED/DC. (later edit: see post 4)

2.)  I re-wrote this as:

Then re-write the sin as a cos:

Square this to remove the root and re-arrange as a quadratic.

(note: because this method has required a step with squaring it is possible the 'answer' won't fit the original question, so check by sunstituing back}

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

DarkTangent

Member

Registered: 2017-07-03

Posts: 20

Re: Trigonometry

1.)

2.)

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All our dreams can come true if we have the courage to pursue them - Walt Disney

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Trigonometry

hi DarkTangent

(1) Whoops, my mistake, sorry.  I was trying to find tan BCD.  For BDC work out tan BDA and then use the formula tan (180 - θ) = - tan (θ )

For (2) it looks like you may just have a simple error somewhere with the working as that result has features that suggest to me you are on the right lines.  If you post your working I'll try to spot what went wrong.  I'm confident about my answer for this one because when I substituted back the expression evaluated to 2.

Bob

---

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

DarkTangent

Member

Registered: 2017-07-03

Posts: 20

Re: Trigonometry

1.)

2.)

---

All our dreams can come true if we have the courage to pursue them - Walt Disney

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Trigonometry

(1)  I think that answer is correct.

(2)  Did you get a quadratic? And if so, please post it.

Bob

---

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

DarkTangent

Member

Registered: 2017-07-03

Posts: 20

Re: Trigonometry

1.) It's correct! Thanks!

2.)

Last edited by DarkTangent (2017-09-05 06:26:58)

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All our dreams can come true if we have the courage to pursue them - Walt Disney

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Trigonometry

That's correct!  Well done.

Bob

---

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

DarkTangent

Member

Registered: 2017-07-03

Posts: 20

Re: Trigonometry

Thanks a lot for your help! I really appreciate it!

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All our dreams can come true if we have the courage to pursue them - Walt Disney