2 answers:
Let x be the measure of angle BAC. Since this is an isosceles triangle, the measure of BCA is equal to BAC.
x+x+90 = 180
2x+90-90 = 180-90
2x = 90
2x/2 = 90/2
x = 45
The two angles BAC and BCA are each 45 degrees. This is a 45-45-90 triangle
The answers to part A and B are the same: 45 degrees
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For parts C and D, the answers are also the same as well. This is because AB = BC in this isosceles triangle
AC = AB*sqrt(2)
10 = x*sqrt(2)
10/sqrt(2) = x*sqrt(2)/sqrt(2)
x = 10/sqrt(2)
x = 10*(1/sqrt(2))
x = 10*(sqrt(2)/2)
x = 5*sqrt(2)
AB is exactly 5*sqrt(2) units long
AB is approximately 7.0710678 units long
AB = BC so BC is also approximately 7.0710678 units long
C. length of AB i think so
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