Posted by Steven on Wednesday, March 9, 2011 at 10:00pm.
I have a isosceles trapezoid question. The top line is 13" long, the sides are 60" long, and the bottom is 27" long. I do not know what is the equation or formula is to determine the acute angle between the bottom and sides or top and sides. Can you please let me know what the equation or math formula is?
- geometry - Reiny, Wednesday, March 9, 2011 at 10:46pm
draw in a diagonal, let its length be x
Since you have parallel lines, alternate angles are equal, let that angle be Ø
we can use the cosine law twice
1. 60^2 = x^2 + 13^2 - 2(x)(13)cosØ
cosØ = (x^2 + 169 - 3600)/(26x)
2. 60^2 = x^2 + 27^2 - 2(x)(27)cosØ
cosØ = (x^2 + 27^2 - 3600)/(54x)
then (x^2 - 3431)/(26x) = (x^2 - 2871)/(54x)
(x^2 - 3431)/(26) = (x^2 - 2871)/(54) , after multiplying both sides by x
54x^2 - 185274 = 26x^2 - 74646
28x^2 = 110628
x^2 = 3951
x = 62.857
put that back into one of the first two equations, to get cosØ, and then Ø
then use the Sine Law to get a 2nd angle in one of the triangles.
check my arithmetic.
- geometry - tchrwill, Thursday, March 10, 2011 at 10:19am
The lower angle derives from arcos[(27-13)/2]/60 = 83.3º.
The upper angle is therefore 96.7º.
Answer This Question
More Related Questions
- geometry - ABCD is an isosceles trapezoid with a height of 4 inches and bases of...
- Geometry Question (multiple choice)! - The isosceles trapezoid is part of an ...
- math - so if a trapezoid has 4 sides and the top(short) side and the two not ...
- Help me - 11. Name the triangles that are classified by angles. right, scalene, ...
- Pre Calc - I have no idea how to do this problem I thought you would have to do ...
- math - a college football pennant is in the shape of an isosceles traingle . the...
- geometry - the longer base of an isosceles trapezoid is 14 feet. the nonparallel...
- geometry - am building a birdhouse. the bottom is 5" wide by 7" long. the sides...
- Geometry - Write proof for the following Given: line AC is congruent to line BD...
- Geometry - Write a proof for the following Given: line AC is congruent to line ...