Answer:
D
21√2/2
C
C
C
Step-by-step explanation:
For all problems, the ratios of the lengths of the sides are:
30-60-90 triangle 1 : √3 : 2
45-45-90 triangle 1 : √2 : √2
Problem 3:
30-60-90 triangle at left
Hypotenuse = 11
Short leg = 11/2
Long leg = 11/2 × √3
45-45-90 triangle at right
x = 11/2 × √3 × √2 = 11√6/2
Answer: D
Problem 4:
30-60-90 triangle at top
Hypotenuse = 7√3
Short leg = 7√3/2
Long leg = 7√3/2 × √3 = 7 × 3/2 = 21/2
45-45-90 triangle at right
x = 21/2 × √2 = 21√2/2
Answer: 21√2/2
Problem 7:
30-60-90 triangle
Long leg = 4√3
Short leg = y = 4√2/2 = 2√2
Answer: C.
Problem 6:
30-60-90 triangle at left
Hypotenuse = 12√6
Short leg = 12√6/2 = 6√6
Long leg = 6√6 × √3 = 6√2√3√3 = 18√2
45-45-90 triangle at right
x = 18√2/√2 = 18
Answer: C.
Problem 8:
45-45-90 triangle
Hypotenuse = 2
Leg = y = 2/√2 = 2√2/(√2√2) = √2
Answer: C.
