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
andre [41]
2 years ago
10

B) T is due north of C, calculate the bearing of B from C

Mathematics
1 answer:
choli [55]2 years ago
7 0

Answer:

(a) 52°

(b) 322°

Step-by-step explanation:

(a) The details of the circle are;

The diameter of the circle = AOC

The center of the circle = Point O

The point the line AT cuts the circle = Point B

The point the tangent PT touches the circle = Point C

Angle ∠COB = 76°

We have that angle AOB and angle COB are supplementary angles, therefore;

∠AOB + ∠COB = 180°

∠AOB = 180° - ∠COB

∴ ∠AOB = 180° - 76° = 104°

∠AOB = 104°

OA = OB = The radius of the circle

Therefore, ΔAOB  =  An isosceles triangle

∠OAB = ∠OBA by base angles of an isosceles triangle are equal

∠AOB + ∠OAB + ∠OBA = 180° by angle summation property

∴ ∠AOB + ∠OAB + ∠OBA = ∠AOB + ∠OAB + ∠OAB = ∠AOB + 2×∠OAB = 180°

∠OAB = (180° - ∠AOB)/2

∴ ∠OAB = (180° - 104°)/2 = 38°

∠TAC = ∠OAB = 38° by reflexive property

AOC is perpendicular to tangent PT at point C, by tangent to a circle property, therefore;

∠TCA = 90° and ΔTCA = A right triangle

∠TAC + ∠ATC + ∠TCA = 180° by angle sum property

∠ATC = 180° - (∠TAC + ∠TCA)

∴ ∠ATC = 180° - (38° + 90°) = 52°

Angle ATC = 52°

(b) In ΔABC, ∠ABC = Angle subtended by the diameter = 90°

∴ ΔABC = A right triangle

∠ABC and ∠TBC are supplementary angles, therefore;

∠ABC + ∠TBC = 180°

∠TBC = 180° - ∠ABC

∴ ∠TBC = 180° - 90° = 90°

∠TCB = 180° - (∠TBC + ∠ATC)

∴ ∠TCB = 180° - (90° + 52°) = 38°

The bearing of B from C = (360° - 38°) = 322°.

You might be interested in
What is the answer to 1-5
34kurt

1. EFG

2. F

3. FA and FB Take a moment to look at this one. The two rays are pointing in opposite directions. They are 180o apart. They share a common point at F.

FE and FG does the same thing.

4. No G is on a line that has only one point on the plane and that point is F.

5, AC has an infinite number of points on the plane.

5 0
3 years ago
Joe has 5 dimes and 4 pennies. Jamal has 2 dollars, 4 dimes, and 5 pennies. Jimmy has 6 dollars and 4 dimes. They want to put th
sesenic [268]

Answer:

no they had $9.39

Step-by-step explanation:

i just added them all together

3 0
3 years ago
Which expression is equivalent to (x - 5)(4x2 – 3x + 8)?
ruslelena [56]

Answer:

(x - 5) (x (4 x - 3) + 8)

Step-by-step explanation:

4 x^3 - 23 x^2 + 23 x - 40

x (x (4 x - 23) + 23) - 40

(x - 5) (x (4 x - 3) + 8)

6 0
3 years ago
What is the equation of a line that is parallel to -x+3y=6 and passes through the point (3,5)?
Elena-2011 [213]

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

Where:

m: It's the slope

b: It is the cut-off point with the y axis

By definition, if two lines are parallel then their slopes are equal.

We have the following line:

-x + 3y = 6\\3y = x + 6\\y = \frac {1} {3} x + \frac {6} {3}\\y = \frac {1} {3} x + 2

Thus, the slope is:m_ {1} = \frac {1} {3}

Then m_ {2} = \frac {1} {3}

So, the line is of the form:

y = \frac {1} {3} x + b

We substitute the point(x, y) :( 3,5)and find b:

5 = \frac {1} {3} (3) + b\\5 = b

Thus, the equation is:

y = \frac {1} {3} x + 5

Answer:

y = \frac {1} {3} x + 5

5 0
3 years ago
Please that (b).​​ I'm having some difficulties.​​
nata0808 [166]

Here's the answer.

Hope it helps u.

:)

7 0
3 years ago
Other questions:
  • This week, Conrad will work 1 3/4 times as long as last week. Giovanni will work 1 1/3 times as last week. Sally will work 2/3 o
    14·1 answer
  • The length of one base of a trapezoid is 19 less than five times the length of the other base. If the trapezoid has a height of
    6·1 answer
  • Julie tried to use the law of syllogism to draw a conclusion based on the statements below. Explain why she is not able to do so
    8·2 answers
  • The table shows the results of a random survey of people about their favorite movie genres.
    9·2 answers
  • Write thThe bookstore is selling a series of 4 books for $97.50. What is the unit price for one book? Round your answer to the n
    6·1 answer
  • I am attaching the question
    5·1 answer
  • Jacob is planting flowers in his yard. He Goes to a Nursery to purchase flowers he decided to purchase petunias and sunflowers p
    6·1 answer
  • Question in attachment!​
    12·1 answer
  • Cherry Avenue Park is in the shape of a rectangle. What is the area, in square
    9·1 answer
  • Write an expression for the sequence of operations described below.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!