1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tester [92]
2 years ago
10

Find Sin (BAC+30) 80POINTS

Mathematics
2 answers:
gogolik [260]2 years ago
8 0

sin<BAC

  • P/H
  • 16/20

cos<BAC

  • B/H
  • 12/20

NOw

  • sin(<BAC+30)
  • sin<BAC×cos30+cos<BACsin30
  • 16/20(√3/2)+12/20(1/2)
  • 2/5√3+3/10
Ann [662]2 years ago
3 0

Answer:

\dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}

Step-by-step explanation:

<u>Trigonometric Identities</u>

\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

Using the trig ratio formulas for cosine and sine:

  • \cos (\angle BAC)=\dfrac{12}{20}
  • \sin (\angle BAC)=\dfrac{16}{20}

<u>Angles</u>

\sin (30^{\circ})=\dfrac{1}{2}

\cos (30^{\circ})=\dfrac{\sqrt{3}}{2}

Therefore, using the trig identities and ratios:

\begin{aligned}\sin (\angle BAC + 30^{\circ}) & = \sin (\angle BAC) \cos (30^{\circ})+\cos (\angle BAC) \sin (30^{\circ})\\\\& = \dfrac{16}{20} \cdot \dfrac{\sqrt{3}}{2} + \dfrac{12}{20} \cdot \dfrac{1}{2}\\\\& = \dfrac{16}{40}\sqrt{3}+\dfrac{12}{40}\\\\& = \dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}\end{aligned}

You might be interested in
pls help!? with all 4 Questions I would rlly appreciate your help thx to plp who help me I will improve on my math and be way be
aliina [53]
7.6=w/12
w=7.6(12)
w=91.2

x/2=20
x=20(2)
x=40

8.3x=41
x=41(8.3)
x=340.3

54=r/3
r=54(3)
r=162








6 0
3 years ago
HELP PLEASE!! Algebra II
butalik [34]

Answer:

Step-by-step explanation:

J is correct.. that function can never be less than 2

7 0
3 years ago
Read 2 more answers
A set of cards contains the numbers 1 through 20. Mathieu chooses a card at random, records the number of the card, and then ret
Vitek1552 [10]

Answer:

20

Step-by-step explanation:

6 0
2 years ago
What is the sum of the interior angles of the polygon pictured below?
kkurt [141]

3420°

explanation:

the equation of the sum of interior angles are (n-2)x180

polygon above has 21 sides so you sub n as 21 and plug the equation in the calculator

8 0
3 years ago
Read 2 more answers
Rewrite by completing the square 2x^2+7x+6=0
Kitty [74]

Answer:

2x^2+7x+6=0\\\\2(x^2+\frac72x+3)=0\\\\2[x^2+2\cdot x\cdot\frac74+(\frac74)^2-(\frac74)^2+3]=0\\\\2[x^2+2\cdot x\cdot\frac74+(\frac74)^2]-2(\frac74)^2+6=0 \\\\2(x+\frac74)^2-2\cdot\frac{49}{16}+6=0\\\\2(x+\frac74)^2-\frac{49}8+\frac{48}8=0\\\\2(x+\frac74)^2-\frac18=0

6 0
3 years ago
Other questions:
  • 7 POINTS!!! ~ A 6 foot tall man casts a shadow that is 4.5 feet long. A telephone pole casts a shadow that is 15.6 feet long. Tw
    15·1 answer
  • Let ƒ(x) = x + 1 and g(x) = 5x. Evaluate the composition (ƒ ∘ g)(–1). Question 2 options: A) (ƒ ∘ g)(–1) = 6 B) (ƒ ∘ g)(–1) = –4
    15·1 answer
  • What is the solution to the equation 3(2x+5)=3x+4x<br> A.x=0<br> B.x=4<br> C.x=5<br> D.x=15
    9·2 answers
  • How many times does 85 go into 221<br> Explain Thx!!
    8·2 answers
  • A certain car in Canada can travel 15 kilometers per 1 liter of gasoline.How many miles per gallon is this.Round to the nearest
    5·1 answer
  • How many miles per hour is 350 km/h?
    12·1 answer
  • 9. 1/3(x+6) =8
    10·2 answers
  • Math hey guys can somebody please help me out here
    9·1 answer
  • Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
    9·2 answers
  • What is the length of the hypotenuse? If necessary, round to the nearest tenth.
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!