Finding Side AB and Angle ABC of a Park Problem

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In summary, Ok my math is a little rusty. I ran across a problem that states:"A park is being considered in a space between a small river and a highway as a rest stop for travelers. Boundary BC is perpendicular to the highway and boundary AD makes an angle of 75 Deg. with the highway. BC= 160.0 m , AD= 270.0 m, and the boundary along the highway = 190.0m long. What are the length of side AB and the magnitude of angle ABC?"The problem asks for the length of side AB and the magnitude of angle ABC. The answer to the problem is that the length of side AB is 160.0 meters and the magnitude of angle
  • #1
ur5pointos2sl
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Ok my math is a little rusty. I ran across a problem that states:
"A park is being considered in a space between a small river and a highway as a rest stop for travelers. Boundary BC is perpendicular to the highway and boundary AD makes an angle of 75 Deg. with the highway. BC= 160.0 m , AD= 270.0 m, and the boundary along the highway = 190.0m long. What are the length of side AB and the magnitude of angle ABC?"

I have attached a file that is almost identical to the one in the book. I need help figuring out where to start this problem(not an answer please). Any help would be appreciated.

Thanks
 

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  • #2
Welcome to PF!

ur5pointos2sl said:
"A park is being considered in a space between a small river and a highway as a rest stop for travelers. Boundary BC is perpendicular to the highway and boundary AD makes an angle of 75 Deg. with the highway. BC= 160.0 m , AD= 270.0 m, and the boundary along the highway = 190.0m long. What are the length of side AB and the magnitude of angle ABC?"

Hi ur5pointos2sl ! Welcome to PF! :smile:

I can't see your picture file yet, but I think the best way is probably to use x and y coordinates, starting with C as the origin. :wink:
 
  • #3
My problem is that I can't seem to use law of sine/cosine because there is always 2 things to be solved for. I think I am missing something.

I put C at the origin and looked at it that way. If i separate the figure into two triangles that doesn't seem to lead me anywhere either. I can solve for one but then the other I am completely stuck on.
 
  • #4
You don't need coordinates. DO split the quadrilateral into two triangles. Solve the right triangle first. Find length of BD and the two angles. Then you have side-angle-side on the remaining triangle. Solve it.
 
  • #5
You don't need coordinates. DO split the quadrilateral into two triangles. Solve the right triangle first. Find length of BD and the two angles. Then you have side-angle-side on the remaining triangle. Solve it.

Thank you. That is exactly what I did last night except I solved for the right triangle then used law of cosine to solve for the other. I finally realized my answer was off because I was rounding to one decimal place.
 

FAQ: Finding Side AB and Angle ABC of a Park Problem

1. How do I find the side length of AB in a park problem?

To find the side length of AB, you will need to use the Pythagorean Theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. So, you can set up an equation using this theorem and solve for the length of AB.

2. What information do I need to find the angle ABC in a park problem?

To find the angle ABC, you will need to know the lengths of all three sides of the triangle. This can be done using the Pythagorean Theorem or by using trigonometric functions such as sine, cosine, or tangent.

3. Can I use a protractor to measure the angle ABC in a park problem?

Yes, you can use a protractor to measure the angle ABC in a park problem. However, this will only give you an estimate of the angle. To find the exact measure of the angle, you will need to use the lengths of the sides and trigonometric functions.

4. How do I use the information about side AB and angle ABC to solve a park problem?

To solve a park problem, you will need to use the information about side AB and angle ABC to find the missing side lengths or angles of the triangle. This information can also be used to determine the area or perimeter of the triangle, depending on the specific problem.

5. Are there any other methods to find side AB and angle ABC in a park problem?

Yes, there are other methods to find side AB and angle ABC in a park problem. Some of these methods include using the Law of Sines, Law of Cosines, or geometric constructions. However, the most commonly used method is using the Pythagorean Theorem and trigonometric functions.

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