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
Hoochie [10]
3 years ago
13

Vertices A and B of triangle ABC are on one bank of a river, and vertex C is on the opposite bank. The distance between A and B

is 200 feet. Angle A has a measure of 33°, and angle B has a measure of 63°. Find b. 110 ft
168 ft
179 ft
223 ft

Mathematics
1 answer:
Anna71 [15]3 years ago
7 0

Answer:

The length of side b is 179 ft

Step-by-step explanation:

Given triangle ABC in which  

∠A = 33°, ∠B = 63°, c=200

we have to find the length of b

In ΔABC, by angle sum property of triangle

∠A+∠B+∠C=180°

33°+63°+∠C=180°

∠C=180°-33°-63°=84°

By sine law,

\frac{\sin \angle A}{a}=\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}

\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}

\frac{\sin 63^{\circ}}{b}=\frac{\sin 84^{\circ}}{200}

b=200\times \frac{\sin 63^{\circ}}{\sin 84^{\circ}}=179.182887\sim 179 ft

The length of side b is 179 ft

Option C is correct.

You might be interested in
the second of two number is 6 more than 3 times the first. The sum of the two number is 30. Find the two numbers​
pantera1 [17]

Answer:

kinda hard

Step-by-step explanation:

7 0
3 years ago
Sam earned $40 on his investment of $400. He earned 5% interest on his investment. How long did Sam leave his money in the bank?
gogolik [260]

Answer:

2yrs

Step-by-step explanation:

Given parameters:

Amount of interest earned  = $40

Principal  = $400

Interest rate  = 5%

Unknown:

Time taken for the money to be in bank = ?

Solution:

   The formula for interest is given as:

         I = \frac{PRT}{100}  

    Where I is the interest

              P is the principal

               R is the rate

               T is the time

    So;

    100I  = PRT

       T  = \frac{100I }{PR}   = \frac{100 x 40}{400 x 5}  = 2yrs

8 0
2 years ago
Please help I'll give brainliest
Hoochie [10]
You have to multiply by how many months or boxes and your gonna have 360 and your friend 288
5 0
3 years ago
The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.
MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle =3\times\ side

3\times\ side =[tex]81\sqrt{3}

Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm

Thus from the diagram , Side AB=BC=AC= 27\sqrt{3} \ cm

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus \angle OBC = 30°

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2}  } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\

Thus ,apothem  OE= 13.5 cm

Now for radius,

We consider ΔOBE

cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB}  \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

4 0
3 years ago
Which of these is true? A) 357 > 571 B) 432 > 571 C) 571 > 432 D) 571 < 357
elena55 [62]
Answer is C) 571>432
4 0
3 years ago
Other questions:
  • Look at picture for question and answer
    5·1 answer
  • Billy and Maria ordered flyers to advertise the school dance. Flyers cost $8.75 for the
    15·1 answer
  • Explain how to estimate 524 divide 9
    5·1 answer
  • solve the below systems of equations using linear combination method. 2x + 3y =1. and y= -2x - 9. explain
    10·1 answer
  • Angela has 15 chocolate cookies. She eats 6 of them, then goes to the store and buys 1 more. How many cookies does Angela have n
    11·1 answer
  • A pair of sunglasses on sale for 30% off original price.if the original Price is $18.00 what is the sale price?
    7·2 answers
  • Casey invested $1,225 in a certain bond that pays 19% interest compounded annually. How long will it take for Brad’s investment
    14·1 answer
  • -2x+19+12x=49 solve for x
    5·2 answers
  • Simplify this complex fraction (GIVE AN EXPLANATION)
    15·2 answers
  • What is the measure of VKW?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!