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:
-2-2√3, -2+2√3
Step-by-step explanation:
Let x represent one of the numbers. Then the other number is -4-x. We want the product to be -8:
x(-4-x) = -8
-4x -x^2 = -8 . . . . . eliminate parentheses
x^2 +4x = 8 . . . . . . multiply by -1
x^2 +4x +4 = 12 . . . add 4 to complete the square
(x +2)^2 = 12
x +2 = ±√12 = ±2√3
x = -2±2√3
The two numbers are -2-2√3 ≈ -5.4641, and -2+2√3 ≈ 1.4641.
Answer:
21 cm
Step-by-step explanation:
Since this is an isosceles triangle, the two sides with a line through them must have the same value of x. Therefore, you can set up the following equation:
2x+11=53
2x=42
x=21 cm
Hope this helps!
Answer:
D. sin m∠C = 2 square root of 5 all over 5
Step-by-step explanation:
The triangle ABC is a right angled triangle. The angle ∠C is where we are asked to find. The side AB measures 6 , AC measures 3 and the side BC measures 3√5.
The longest side of a right angle triangle is the hypotenuse, that means the side with length 3√5 is the hypotenuse.
Therefore side BC is the hypotenuse side and we are asked to find the angle C. AB is the opposite side while AC is the adjacent side.
Using
sin C = opposite/hypotenuse = 6/3√5 = 2/√5 = 2√5/5
cos C = adjacent/hypotenuse = 3/3√5 = 1/√5
Answer:
Charlie by 60 words more.
Step-by-step explanation:
60 x 30 = 180
40 x 30 = 120
180 - 120 = 60
