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 Brianna�fs house. The measure NBA�Ú as and �‹75BAN�Úas. Determine the distance between their houses.

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 Brianna�fs house. The measure NBA�Ú as and �‹75BAN�Úas."

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.

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).

Thank you, that's what I got too:)

Good!

You're welcome!

richard is standing between two buildingd

To clarify the question, point A is not the waterpark itself. Point A is a point along the edge of the waterpark, 120 meters away from Brianna's house. The distance you need to calculate is the distance between Noah's house and Brianna's house.

To draw a diagram for this question, you can start by drawing a line segment to represent the edge of the waterpark. Label one end of the line segment as "B" to represent Brianna's house. Then, mark a point 120 meters along the line segment and label it as "A". Finally, draw a line segment from point A to another point, which represents Noah's house.

Now, to calculate the distance between their houses, we can use the information given about the angles. The angle NBA is given as "as" and the angle BAN is given as "as + 75".

To determine the distance between their houses, you will need to use trigonometry. Specifically, you can use the sine rule to calculate the length of side NA in the triangle NBA. The sine rule states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, you can use the formula:
NA / sin(as) = BA / sin(as + 75)

Since you are given BA as 120 meters, you can rearrange the formula to solve for NA:
NA = BA * sin(as) / sin(as + 75)

Substitute the given values into the formula and calculate NA. Then, add this length to 120 meters to find the total distance between Noah's house and Brianna's house.

By following these steps, you should be able to verify whether your answer of 196.6 meters is correct or not.