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
exis [7]
3 years ago
12

Find all solutions for a triangle with c=70 c=24 and a=25

Mathematics
2 answers:
Slav-nsk [51]3 years ago
5 0

Answer:

see the attachments for the two solutions

Step-by-step explanation:

When the given angle is opposite the shorter of the given sides, there will generally be two solutions. The exception is the case where the triangle is a right triangle (the ratio of the given sides is equal to the sine of the given angle). If the given angle is opposite the longer of the given sides, there is only one solution.

When a side and its opposite angle are given, as here, the law of sines can be used to solve the triangle(s). When the given angle is included between two given sides, the law of cosines can be used to solve the (one) triangle.

___

Here, the law of sines can be used to solve the triangle:

A = arcsin(a/c·sin(C)) = arcsin(25/24·sin(70°)) = 78.19° or 101.81°

B = 180° -70° -A = 31.81° or 8.19°

b = 24·sin(B)/sin(70°) = 13.46 or 3.64

madreJ [45]3 years ago
4 0

Answer:

Value of b is 13 , m∠B = 31° and m∠A = 79°.

Step-by-step explanation:

Given: m∠C = 70°  , c = 24  and a = 25

To find : All solutions of triangle that is m∠B , m∠A and b

We use law of sines which states that the ratio of the length of a side of triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.

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

Consider,

\frac{a}{sin\,A}=\frac{c}{sin\,C}

\frac{25}{sin\,A}=\frac{24}{sin\,70}

sin\,A=\frac{25\times sin\,70}{24}

sin\,A=\frac{25\times0.94}{24}

sin A = 0.98

sin A = sin 79

A = 79° (approx.)

∠A + ∠B + ∠C = 180°   ( Angle Sum Property of triangle )

79 + ∠B + 70 = 180

∠B = 180 - 149

m∠B = 31°

now Consider,

\frac{a}{sin\,A}=\frac{b}{sin\,B}

\frac{25}{sin\,79}=\frac{b}{sin\,31}

b=\frac{25\times sin\,31}{sin\,79}

b=\frac{25\times0.52}{0.98}

b = 13 (approx.)

Therefore, Value of b is 13 , m∠B = 31° and m∠A = 79°.

You might be interested in
Exercise
svp [43]

By addition of all the exercise and substracting it from 1 hourJavier runs on treadmill on Monday is 0.40 hour.

Now According to the question javier completed 3 repetitions of each exercise so by multiplication time taken by javier to complete each exercise is as follow;

Squats = 0.8*3= 0.24 hour

Crunches = 0.03*3 = 0.09 hour

Lunges = 0.04*3 = 0.12 hour

curls = 0.05*3 = 0.15 hour

we can calculate total time taken to complete all exercise by Addition is,

0.24 + 0.09 + 0.12 + 0.15

0.60 hour

time taken on treadmill by javier;

1 hour - 0.60 hour

0.40 hour

Read more about Addition here:

brainly.com/question/20658817

#SPJ4

4 0
1 year ago
Suppose that the handedness of the last fifteen U.S. presidents is as follows:40% were left-handed (L)47% were Democrats (D)If a
lesantik [10]

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Probability that they were left handed P(L)= 40%

Probability that they were Democrats P(D)= 47%

So, P(L∩D) = 135 = 0.13

Now, to check whether they are independent or not.

We will find P(L) × P(D) is given by

P(L)\times P(D)=0.47\times 0.40=0.188

Since P(L) . P(D) ≠ P(L∩D)

So, they are not independent.

Hence, Option 'c' is correct.

3 0
3 years ago
WORTH 20 POINTS PLS HELP!
scZoUnD [109]

Answer:80ft

Step-by-step explanation:

4 0
3 years ago
What is the percentage 23 over 50
fredd [130]
23/50 is 0.46 so the percentage would be 46%
7 0
3 years ago
Read 2 more answers
Estimate a 15% tip on a dinner bill of $72.13 by first rounding the bill amount to the nearest ten dollars?
mixas84 [53]

Answer:

the tip is $10.5 = $72.15= $70*.15+ $10.5

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • Each of the students im Romi's class raised at least $25 during the jump-a-thon. What is the least amount of money the class rai
    13·1 answer
  • A= 158.368 ft2<br><br> Radius=<br><br> Diameter=
    6·1 answer
  • Given A (-3,5) and B (6,7) find AB
    8·1 answer
  • A gardener has three rectangular plots that are adjacent to each other. She has 120 yards of fencing and the total area of the p
    7·1 answer
  • Determine the range of the function graphed above.
    9·1 answer
  • Cual es la historia de las funciones lineales ?
    7·1 answer
  • What are the multiples of 1/5
    8·2 answers
  • Reese is selling lemonade at the parade. He gets to keep 50% of the money he collects. A large lemonade is $8.00 and a small lem
    8·1 answer
  • - Systems of Linear Equations &amp; Inequalities
    6·1 answer
  • A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by th
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!