MATHEMATICS HIGH SCHOOL

Find b, given that a = 20, angle A = 30°, and angle B = 45° in triangle ABC

Answers

Answer 1

Answer:

Answer:

b = 20√2

Step-by-step explanation:

Given: ΔABC

a = 20 , m∠A = 30° and m∠B = 45°

To find: value of b.

We use Sine result, which state that

$(a)/(sin\,A)=(b)/(sin\,B)$

Substituting given values we, get

$(20)/(sin\,30^(\circ))=(b)/(sin\,45^(\circ))$

we know that $sin\,30^(\circ)=(1)/(2)\:and\:sin\,45^(\circ)=(1)/(√(2))$ , we get

$(20)/((1)/(2))=(b)/((1)/(√(2)))$

$20{*2}=b*√(2)$

$b*√(2)=40$

$b=(40)/(√(2))$

$b=20√(2)$

Therefore, b = 20√2

Answer 2

Answer: The side b is opposite to the angle B, applying the law of the sines, we have:

$(a)/(sinA) = (b)/(sinB)$
$(20)/(sin30^0) = (b)/(sin45^0)$
$(20)/( (1)/(2) ) = (b)/( ( √(2) )/(2) )$
$20* ( √(2) )/(2) = b* (1)/(2)$
$(20 √(2) )/(2) = (b)/(2)$
$2*b =2*20 √(2)$
$2b = 40 √(2)$
$b = (40 √(2) )/(2)$
$\boxed{b = 20 √(2) }$

Related Questions

Simplify (3n – 2m)2 = ? a. 6n2 – 12mn – 4m2 b. 9n2 – 12mn – 4m2 c. 9n2 12mn 4m2 d. 9n2 – 12mn 4m2
The table summarizes the scoring of a football game between Team A and Team B. A touchdown (TD) is worth 6 points, a field goal (FG) is worth 3 points, a safety (S) is worth 2 points, and a point after touchdown (PAT) is worth 1 point. Use matrix multiplication to find the final score.TD FG S PAT Team A 3 2 1 0 Team B 4 4 1 2 help is appreciated anyone to help first gets a medal
6(f+4)+2(f+4)
Miller School has 2 boys for every 3 girls in the fifth grade. There are 120 students in the fifth grade. How many girls are there? How many boys are there?
The director of marketing at a large company wants to determine if the amount of money spent on internet marketing is a good predictor of company profit. She fits a least-squares regression line to 20 months of data and computes the following regression line:Profit = 372.6 + 17.2(advertising dollars) What is the value of the residual for advertising dollars spent equal to $1,020 and Profit equal to $17,500? Round to the nearest integer.

Which of the following is not a correct description of the graph of the function y = -2x - 7?(A) The graph of the function contains the point (−2, −3), and when the value of x increases by 1 unit, the value of y decreases by 2 units.
(B) The graph of the function contains the points (−1, −5), (2, −11), and (4, −15).
(C) The graph of the function is a line that passes through the point (0, −7) with a slope of −2.
(D) The graph of the function contains the points (0, −7), (1, −9), and (3, −1).

Answers

Try graphing the function and go over each answer to see whether or not its true

According to the Rational Roots Theorem, which statement about f(x) = 25x^7 – x^6 – 5x^4 + x – 49 is true?Any rational root of f(x) is a multiple of –49 divided by a multiple of 25.

Any rational root of f(x) is a multiple of 25 divided by a multiple of –49.

Any rational root of f(x) is a factor of –49 divided by a factor of 25.

Any rational root of f(x) is a factor of 25 divided by a factor of –49.

Answers

Answer:

Any rational root of f(x) is a factor of -49 divided by a factor of 25.

Step-by-step explanation:

The Rational Root Theorems states that :

If the polynomial $P(x)= a _nx^n +{a_(n-1)x}^(n-1)+............{a_(2)x}^(2)+{a_(1)x}^(1)+a_0$ has any rational roots, then they must be in the form of

$\pm (factors of a_0)/(factors of a_n)$

Consider the polynomial

$f(x)=25x^7-x^6-5x^4+x-49$

in this case, we have $a_0=-49$ and $a_n=25$

Any Rational root of f(x) is a factor of $a_0=-49$ divided by a factor of $a_n=25$

According to the Rational Roots Theorem, the statement about f(x) = 25x^7 – x^6 – 5x^4 + x – 49 which is true is:

Any rational root of f(x) is a factor of –49 divided by a factor of 25.

The key points are "factors", and "ratio between the constant term and the coefficient of the highest order (exponent) term"

Integers are _____ rational numbers
A. always
B. somtimes
C. never

Answers

Integers are always rational!

A rational number is a number that can be expressed as $(p)/(q)$ , where p and q are both integers.

So each integer can be expressed as $(itself)/(1)$ , which is always rational as "itself" if an integer!

If i have all the angles and one side can i find the other sides

Answers

Sure, that's what solving triangles is. Trigonometry has a short menu. Basically we choose between three formulas: Law of Sines, Law of Cosines, Sum of Triangle Angles

The Law of Sines has two sides and two opposite angles; given any three we can solve for the fourth.

The Law of Cosines has three sides and one angle; again given any three we solve for the remaining one.

The Sum of Triangle Angles says all three angles add to 180 degrees, so given two we can find the third.

Here we have all the angles and one side, that's Law of Sines to get the remaining sides.

The amount of light a star gives off is used to determine the star’s a.number of planets
b.position in the galaxy
c.shape
d.brightness

Answers

b. position in the galaxy

i think its b hope this helps

642×50 2 Digit By 3 digit really bad at math sorry

Answers

The answer is 32,100. Don't worry practise will make you better!

the answer would be 32100

Other Questions

The length of a rectangle is 10 feet more than the width. The area of the rectangle is 96 square feet. Find the dimensions of the rectangle. Solve algebraically.

A system of equations is shown below: 5x + 2y = 3 (equation 1) 2x − 3y = 1 (equation 2) A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?

Which statements accurately describe the function f(x) = 3radical18^x? Check all that apply.The domain is all real numbers. The range is y > 3. The initial value is 3. The initial value is 9. The simplified base is . The simplified base is 3.

Determine the type and number of solutions of 7x^2+3x+8=0