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

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 3:48pmIf 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 4:08pmMaybe 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 11:39amThis 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 9:57pmThank you, that's what I got too:)

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

You're welcome!

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

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