Posted by **Dee** on Sunday, August 21, 2011 at 3:07pm.

Hi - I'm having problems drawing a diagram for the following question. The part I find unclear is "they mark a point A, 120 m along the edge of the waterpark from Brianna's house. I'm wondering if point A is the waterpark. See question. My answer to this question was 196.6 meters, please verify if correct...

Noah and Brianna want to calculate the distance between their houses which are opposite sides of a water park. They mark a point, A, 120 m along the edge of the water park from Briannafs house. The measure NBAÚ as and ‹75BANÚas. Determine the distance between their houses.

- math - encoding problem -
**MathMate**, Sunday, August 21, 2011 at 3:48pm
If you use encoding Western ISO 8859-1 (you'll find this in the menu of your browser under view/encoding), then everyone can read your symbols.

As it is, I do not understand the part:

"They mark a point, A, 120 m along the edge of the water park from Briannafs house. The measure NBAÚ as and ‹75BANÚas."

- math -
**Dee**, Sunday, August 21, 2011 at 4:08pm
Maybe all my questions have this problem. THanks for telling me how to fix it. The original question I posted was:

Noah and Brianna want to calculate the distance between their houses which are opposite sides of a water park. They mark a point, A, 120 m along the edge of the water park from Brianna’s house. The measure <NBA as 75 degrees and <BAN as 70 degrees. Determine the distance between their houses.

- math -
**MathMate**, Monday, August 22, 2011 at 11:39am
This requires essentially the solution of a triangle using the sine rule.

First, let us understand the problem by drawing a diagram:

-------------------N--------------------

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~river~~~~~~~~~~~~~~~~~

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

--------------B---n=120----A--------------

Given:

∠NBA=75° = ∠B

∠BAN=70° = ∠A

therefore

∠BNA=180-75-70=35°

(by sum of angles of a triangle =180°)

Distance BA = 120 m = n

Denote the distance NB = a

and the distance AN = b

Using sine rule, we have

n/sin(N) = a / sin(A)

substituting

n=120m

N=35°

A=70°

and solving for a,

a=n*(sin(A)/sin(N)

=120*sin(70)/sin(35)

=196.596

which is the distance between the houses (NOT the width of the river).

- math -
**Dee**, Monday, August 22, 2011 at 9:57pm
Thank you, that's what I got too:)

- math :) -
**MathMate**, Monday, August 22, 2011 at 10:57pm
Good!

You're welcome!

- math -
**Anonymous**, Friday, May 25, 2012 at 11:36pm
richard is standing between two buildingd

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