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
First, find the area of each figure. Then subtract the smaller area from the larger area. Your work should look something like this:
A = l * w
A = 9 * 9
A = 81
This is the area of the smaller square. Now find the area of the larger square.
A = l * w
A = 15 * 15
A = 225
Now subtract the two areas to find the area of the shape that is left when the smaller square is cut out.
225 - 81 = 144
Your final answer should be:
144 in^2
Answer:
Length (in) Width (in)
2 5
4 10
6 15
8 20
Step-by-step explanation:
Answer:5
Step-by-step explanation:
321 123
Answer:
78 stamps
Step-by-step explanation:
50 stamps collected after 3 days
4 stamps added a day
next 7 days added= 7*4= 28 stamps
Total after 10 days= 50+28= 78 stamps
