Answer:
1.
x = 5√3
y = 10
2.
x = 2√33 in.
3.
y = 11√3
x = 22
4.
x = 7√2
5.
x = 3 m
6.
x = 16
y = 16√3
Explanation:
Recall:
30-60-90 triangle ratio of sides: 1 : √3 : 2
45-45-90 triangle ratio of sides: 1 : 1 : √2
Pythagorean theorem: a² + b² = c²
1.
1 : √3 : 2
5 : x : y
1/5 = √3/x
x = 5√3
1/5 = 2/y
y = 10
2.
a² + b² = c²
8² + x² = 14²
64 + x² = 196
x² = 132
x = 2√33 in.
3.
1 : √3 : 2
11 : y : x
1/11 = √3/y
y = 11√3
1/11 = 2/x
x = 22
4.
1 : 1 : √2
7 : 7 : x
1/7 = √2/x
x = 7√2
5.
a² + b² = c²
x² + 4² = 5²
x² + 16 = 25
x² = 9
x = 3 m
6.
1 : √3 : 2
x : y : 32
1/x = 2/32
2x = 32
x = 16
√3/y = 2/32
√3/y = 1/16
y = 16√3