Hi - I'm reposting this thread as there was some encoding issues in previous version that I clarified near bottom. Thanks.
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.
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 Brianna�fs house. The measure NBA�Ú as and �‹75BAN�Úas."
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.
draw the figure.
Then, law of sines.
sinNBA/120 =sinBAN/distance
solve for distance.
and by the way in answer to your previous question, the angle between west and northwest is 45 degrees.
To draw the diagram for this question, follow these steps:
1. Start by drawing two houses on opposite sides of a water park. Label one house as Noah's house and the other as Brianna's house.
2. Draw a line to represent the edge of the water park between the two houses.
3. From Brianna's house, measure 120 meters along the edge of the water park and mark that point as A. Label it as point A.
4. Based on the given angles, use a protractor or compass to draw an angle NBA with a measure of 75 degrees starting from point N (Noah's house). This angle should extend towards the water park, intersecting the line of the water park.
5. Similarly, draw an angle BAN with a measure of 70 degrees starting from point B (Brianna's house). This angle should also extend towards the water park, intersecting the line of the water park.
Now that the diagram is complete, we can move on to solving the problem.
To calculate the distance between Noah and Brianna's houses, you need to find the length of line AB in the diagram. Here's how to do it using solving techniques:
1. Look at the diagram and identify any angles or sides that can be used to apply a trigonometric relationship. In this case, you can use the angles of the triangle to apply the Law of Sines.
2. Label the remaining angles in the triangle: angle BNA and angle ANB.
3. Apply the Law of Sines, which states that the ratio of a side length to the sine of the opposite angle is constant for any given triangle. In this case, you can use the following relationship:
AB / sin(angle BAN) = BN / sin(angle NBA)
4. Substitute the known values:
AB / sin(70°) = BN / sin(75°)
5. Rearrange the equation to solve for AB:
AB = BN * sin(70°) / sin(75°)
6. Substitute the known value for BN. Since BN is the same as the distance from Noah's house to point A (120 m), you have:
AB = 120 * sin(70°) / sin(75°)
7. Use a calculator to find the numerical value of sin(70°) and sin(75°). Then, calculate AB using the formula.
By following these steps, you should be able to calculate the distance between Noah and Brianna's houses, which in this case you found to be approximately 196.6 meters.