Asked by lilly
Two paper strips each 5 cm wide are laid across each other at an angle of 30 degrees. Determine the area of the overlapping area.
I have no idea where to start with this question or how to go on. I know it has to do with cosine or sine law. But what do I do
I have no idea where to start with this question or how to go on. I know it has to do with cosine or sine law. But what do I do
Answers
Answered by
Reiny
take two identical rulers and lay them across each other at 30° to get a mental image of the problem.
Is the overlapping area not a rhombus with acute angles of 30° and obtuse angles of 150° ?
So make that sketch, all 4 sides are equal, label them x
draw a vertical from the obtuse angle to the base, you now have a 30-60-90° triangle where the side opposite the 30° is 5 cm
You should know that the ratio of sides of the 30-60-90 is 1:√3:2
x/√3 = 5/1
x = 5√3
and the area would be base x height
= (5√3)(5) = 25√3
Is the overlapping area not a rhombus with acute angles of 30° and obtuse angles of 150° ?
So make that sketch, all 4 sides are equal, label them x
draw a vertical from the obtuse angle to the base, you now have a 30-60-90° triangle where the side opposite the 30° is 5 cm
You should know that the ratio of sides of the 30-60-90 is 1:√3:2
x/√3 = 5/1
x = 5√3
and the area would be base x height
= (5√3)(5) = 25√3
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.