Answer:
1. x = 2√3 or 3.46
2. y = 4√3 or 6.93
3. z = 4√6 or 9.80
Step-by-step explanation:
1. Determination of the value of x.
Angle (θ) = 60°
Opposite = 6
Adjacent = x
Tan θ = Opposite /Adjacent
Tan 60 = 6 / x
√3 = 6/x
Cross multiply
x√3 = 6
Divide both side by √3
x = 6 / √3
Rationalise
x = (6 / √3) × (√3/√3)
x = 6√3 / 3
x = 2√3 or 3.46
2. Determination of the value of y.
Angle (θ) = 60°
Opposite = 6
Hypothenus = y
Sine θ = Opposite /Hypothenus
Sine 60 = 6/y
√3/2 = 6/y
Cross multiply
y√3 = 2 × 6
y√3 = 12
Divide both side by √3
y = 12/√3
Rationalise
y = (12 / √3) × (√3/√3)
y = 12√3 / 3
y = 4√3 or 6.93
3. Determination of the value of z.
Angle (θ) = 45°
Opposite = y = 4√3
Hypothenus = z
Sine θ = Opposite /Hypothenus
Sine 45 = 4√3 / z
1/√2 = 4√3 / z
Cross multiply
z = √2 × 4√3
z = 4√6 or 9.80
Answer:
The area of the rectangular deck is 36 sq feet.
Step-by-step explanation:
Let the width of the deck = k ft
So, the length of the deck = (4k) ft
Now, perimeter = 30 ft
PERIMETER OF A RECTANGLE = 2(LENGTH + WIDTH)
⇒2( k + 4k) = 30
or, 2 x 5k = 30 ⇒ 10k = 30
⇒ k = 30/10 = 3
So, the width of the deck = k = 3 ft
Length of the deck = 4k = 3 x 4 = 12 ft
Now, AREA OF A RECTANGLE = LENGTH X WIDTH
So, the area of the rectangular deck = 3 ft x 12 ft
= 36 sq feet
Hence, the area of the rectangular deck is 36 sq feet.
Answer:
$3.60
Step-by-step explanation:
25+20=45 (because you need the tax of both)
0.8(45)=3.60 (finding the tax amount)
Y= 4.5 because the length is less than 6=x.
Answer:
50º
Step-by-step explanation:
Angle D & B are vertical angles, meaning they are equal in measure.
So if Angle B = 50º, then Angle D must also be 50º.
Hope this helps! Have a great day!
