Posted by Dee on .
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,
If you use encoding Western ISO 88591 (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,
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,
This requires essentially the solution of a triangle using the sine rule.
First, let us understand the problem by drawing a diagram:
N
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~river~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Bn=120A
Given:
∠NBA=75° = ∠B
∠BAN=70° = ∠A
therefore
∠BNA=1807570=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,
Thank you, that's what I got too:)

math :) 
MathMate,
Good!
You're welcome! 
math 
Anonymous,
richard is standing between two buildingd