Pythagorean theorem quiz

Problem 1:

11^2+y^2=61^2

121+y^2=3721

y^2=3600

y=60

Problem 2:

x=7

y=7sqrt2

Problem 3:

x=3sqrt5

y=3sqrt10

Problem 4:

x=16

y=16

Problem 5:

10^2+5^2=y^2

100+25=y^2

125=y^2

5sqrt5=y

Problem 6:

Since the missing angle is 40 degrees (90+50+40=180), we can find the cosine of 40 and set it equal to the ratio of the adjacent side over the hypotenuse (100ft):

cos(40)=x/100

76.6=x

The height of the tree is around 76.6 ft

Problem 7:

A diagonal in a square produces 45 degree angles, so we can simply divide  20sqrt2 by the sqrt2 to get a side length of 20. Since the perimeter of a square is 4 times the side length, the perimeter is 20*4 or 80 units.

Problem 8:

8^2+9^2=11^2

64+81=121

145>121

Since the squares of each side length are more than the hypotenuse, the triangle is obtuse.

y = i/2 xtnop + (3i/2 tnop+ 1)

step-by-step explanation:

the picture is the step by step explanation.