3 years ago

Geometry help please

2 answers:

4 0

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