Answer:
√(2 + √3)/4
Step-by-step explanation:
Sine 5π/12 = Sine (5π/6)/2
Recall
π = 180°
Thus,
Sine (5π/6)/2 = Sine (5×180 /6)/2
= Sine 150/2
Recall
Sine θ/2 = √(1 – Cos θ)/2
Thus,
Sine 150/2 = √(1 – Cos 150)/2
But, Cosine is negative in the 2nd quadrant. Thus,
Cos 150 = – Cos 30 = –√3/2
Thus,
√(1 – Cos 150)/2 = √(1 – –√3/2 )/2
= √(1 + √3/2 )/2
= √[(2 + √3)/2 ÷ 2]
= √[(2 + √3)/2 × 1/2]
= √(2 + √3)/4
Therefore,
Sine 5π/12 = √(2 + √3)/4
Answer:
1.25,but your teacher is prolly looking for a fraction so 1 1/4
Step-by-step explanation:
DO NOT PUT 20 THAT PERSON S WRONG
Answer:
Step-by-step explanation:
From the picture attached,
∠4 = 45°, ∠5 = 135° and ∠10 = ∠11
Part A
∠1 = ∠4 = 45° [Vertically opposite angles]
∠1 + ∠3 = 180° [Linear pair of angles]
∠3 = 180° - ∠1
= 180° - 45°
= 135°
∠2 = ∠3 = 135° [Vertically opposite angles]
∠8 = ∠5 = 135° [Vertically opposite angles]
∠5 + ∠6 = 180° [Linear pair of angles]
∠6 = 180° - 135°
∠6 = 45°
∠7 = ∠6 = 45° [Vertically opposite angles]
By triangle sum theorem,
m∠4 + m∠7 + m∠10 = 180°
45° + 45° + m∠10 = 180°
m∠10 = 180° - 90°
m∠10 = 90°
m∠10 = m∠12 = 90° [Vertically opposite angles]
m∠10 = m∠11 = 90° [Given]
Part B
1). ∠1 ≅ ∠4 [Vertically opposite angles]
2). ∠7 + ∠5 = 180° [Linear pair]
3). ∠9 + ∠10 = 180° [Linear pair]
Answer:
KF = 35
Step-by-step explanation:
Since it's a line with K in the middle, we know that the distance SF is the same as SK + KF.
(Start at S, first go to K, then continue to F. You've traveled the same distance as from S to F.)
SF = SK + KF
Let's put in the values we got.
5x + 2 = 27 + (3x -1)
Opening the parenthesis.
5x + 2 = 27 + 3x - 1
5x + 2 = 26 + 3x
Now let's subtract 3x from both sides.
2x + 2 = 26
Now, subtract 2 from both sides.
2x = 24
If we divide by 2...
x = 12
We know that...
KF = 3x -1
Since x is 12, let's put that in.
KF = 3 * 12 - 1 = 36 - 1 = 35
Answer: KF is 35 !
