Answer/Step-by-step explanation:
✔️Using trigonometric ratio, find b:
Reference angle = 45
opposite = 8
Hypotenuse = b
Thus,
Sin(45) = 8/b
b = 8/sin(45)
b = 8/(1/√2) (sin 45 = 1/√2)
b = 8 × √2/1
b = 8√2
✔️Find a using trigonometric ratio:
Reference angle = 60°
Hypotenuse = b = 8√2
Adjacent = a
Therefore,
Cos(60) = a/8√2
8√2*cos(60) = a
8√2*½ = a
4√2 = a
a = 4√2
✔️Find c using Pythagorean Theorem:
c² = b² - a²
c² = (8√2)² - (4√2)²
c² = 128 - 32
c² = 96
c = √96
c = √(16*6)
c = 4√6
<ABC + <ABC = 180
3x- 9 + 7x - 1 = 180
10x - 10 = 180
10x = 190
x = 19
<ABC = 3x- 9 = 3(19) - 9 = 48
Answer:
102
Step-by-step explanation:
The least common multiple of 6 and 17
For us to determine the L.C.M of 6 and 17,
First find the prime factors of 6 and 17
Prime Factor of 6
6 = 2 × 3
Prime factor of 17
17 = 1 × 17
Secondly;
Multiply all the factors together to find the L.C.M:
L.C.M = 1 × 2 × 3 × 17
L.C.M = 102
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(-16+12)/(-4+2)= (-4)/(-2)= 2
Length of Side: 8.5
Perimeter of square: 34
