Applying the trigonometry ratio and rationalization, the missing lengths are:
1. x = 12/√3; y = 2√3
2. x = 5√2; y = 5√2
3. b = 24
4. 4√3
5. 5√3
<h3>What are the Trigonometry Ratio?</h3>
The trigonometry ratios are represented as follow:
- SOH is sin ∅ = opp/hyp
- CAH is cos ∅ = adj/hyp
- TOA is tan ∅ = opp/adj.
1. To find x, apply SOH:
opp = 6
hyp = x
adj = y
∅ = 60°
Equation:
sin 60 = 6/x
x = 6/sin 60
x = 6/√3/2 (sin 60 = √3/2)
x = 6 × 2/√3
x = 12/√3
Rationalize
x = 12/√3 × √3 /√3
x = 12√3/3
x = 4√3
To find y, apply TOA:
tan 60 = 6/y
y = 6/tan 60
y = 6/√3 (tan 60 = √3)
Rationalize
y = 6/√3 × √3 /√3
y = 6√3 / 3
y = 2√3
2. To find x, apply SOH:
opp = x
hyp = 10
adj = y
∅ = 45°
Equation:
sin 45 = x/10
x = (10)(sin 45)
x = 10 × 1/√2 (sin 45 = 1/√2)
x = 10/√2
Rationalize
x = 10/√2 × √2 /√2
x = 10√2/2
x = 5√2
To find y, apply CAH:
cos 45 = y/10
y = (10)(cos 45)
y = 10 × 1/√2 (cos 45 = 1/√2)
y = 10/√2
Rationalize
y = 10/√2 × √2 /√2
y = 10√2/2
y = 5√2
3. To find b, apply Pythagorean theorem:
b = √(25² - 7²)
b = 24
4. 12/√3
Rationalize
12/√3 × √3 /√3
12√3/3
4√3
5. 15/√3 × √3 /√3
15√3 /3
5√3
Learn more about trigonometry ratios on:
brainly.com/question/10417664
Answer:
<em>C: The shark weighs 2200 pounds more than the whale.</em>
Step-by-step explanation:
So you have to remember first that one ton is equal to 2,000 pounds. Then, we convert tons to pounds (for the whale) to get 4(2,000)=8,000 pounds. So, the whale weighs 8,000 pounds. The shark weighs 10,200 pounds, so all you have to do now is do 10,200-8,000 to get 2,200 pounds. So, the answer is C.
Highest common factor of 24 and 56 is 8, 24+56 is 80, 80 over 8 is 10 rows
Answer:
D
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
Here (a, b ] = [ 1, 3 ], thus
f(b) = f(3) = 5 ← from graph
f(a) = f(1) = - 3 ← from graph
average rate of change = 
= 
= 4 → D
