Quad ABCD with diagonal DB. <adc=90, <c=91, <cbd=43. segment ad=segment dc=9.
Which segment is longer ab or ad and why?
by the law of sines, the side opposite the larger angle has the larger length.
How are you solving for <abd. Making assumptions?
by law of sines,
bd/sin91 = 9/sin43
bd = 13.19
by law of cosines,
ab^2 = 9^2 + bd^2 - 2(9)(bd)cos44
= 81 + 174 - 170.84
ab = 9.17
Looks like ab > ad
Thank you steve, but something must be wrong with this problem. We have not learned law of cosines or law of sines yet and the correct answer is ad?? Baffled at how to get this based on what we are studying, SAS and SSS inequality theorems.
Hmmm. If <C were also 90, then DA would be parallel to BC. In that case triangles ADB and DCB would be congruent, and ABCD would be a square, with ad=ab. But that would also require <cbd to be 45, not 43.
So, since <cbd is less than 45, bc > ad, so also ab > ad.
I still don't get ad > ab.
Also, since SAS and SSS are for congruency, not sure how they apply in determining inequality here.
To determine whether segment AB or segment AD is longer, we need to compare their lengths.
Let's analyze the information given:
1. Quad ABCD with diagonal DB: This means that diagonal DB connects two opposite vertices of the quadrilateral formed by A, B, C, and D.
2. <ADC = 90 degrees: This angle is formed by the diagonal and one side of the quadrilateral.
3. <C = 91 degrees: This angle is opposite to side CD.
4. <CBD = 43 degrees: This angle is formed by side CB and diagonal DB.
5. Segment AD = Segment DC = 9: This means that side AD and side DC (adjacent sides of the quadrilateral) have the same length, which is 9 units.
To determine which segment is longer, AB or AD, we need to consider the properties of quadrilaterals and the information given.
1. Since diagonal DB is present, we can conclude that the quadrilateral ABCD is a kite. In a kite, the non-adjacent sides are equal in length. In this case, side AB and side BC are non-adjacent sides.
2. If side AB and side BC are equal in length, and <C = 91 degrees, it means that <ABC is also 91 degrees (since the angles of a triangle adds up to 180 degrees).
3. Considering that <C = 91 and <ABC = 91, we can conclude that <ADC is 180 - 91 - 91 = 180 - 182 = -2 degrees. However, angles cannot be negative, so there seems to be an error in the given information.
Based on the information provided, it is not possible to definitively determine which segment, AB or AD, is longer.