MATHEMATICS HIGH SCHOOL

a=13 c=15 A=53 Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results.

Answers

Answer 1

Answer:

Answer:

The given measurement will produce only 1 triangle

Step-by-step explanation:

Given:

a = 13

c = 15

∠A = 53°

now, applying the law of sine, we have

(a/sinA) = (c/sinC)

on substituting the values, we get

(13/sin53°) = (15/sinC)

sinC = 0.921

C = 67.14°

also, sum of all the angles of a triangle = 180°

thus,

∠A + ∠B + ∠C = 180°

53° + 67.14° + ∠B = 180°

∠B = 59.85°

now,

again applying the law of sine, we have

(a/sinA) = (b/sinB)

on substituting the values, we have

(13/sin53) = (b/sin59.85°)

b = 14.07

now, we have all the dimension of the triangle and have obtained the unique values,

Therefore, the given measurement will produce only 1 triangle

Related Questions

The sum of 3 consecutive integers is 90. find the largest integer if x is the smallest integer
What is the area of this polygon?
TSU is shownWhat are the missing side length inTSU? Show all work? keep your answer in simplified radical form.
The diameter of a Frisbee is 12 in. What is the area of the Frisbee?a. 37.68 sq. in.b. 452.16 sq. in.c. 18.84 sq. in.d. 113.04 sq. in.
Simplify -2xy+3x-2xy+3x

Vanessa ate 2 slices of cake. ishaan ate 1 slice. if there were 1 slice remaining and all the slices were the same size, what fraction of the cake was eaten?

Answers

Answer:

$(3)/(4)$ part of cake was eaten

Step-by-step explanation:

Given: Vanessa ate 2 slices of cake. ishaan ate 1 slice. there were 1 slice remaining.

To Find: If all the slices were the same size, what fraction of the cake was eaten.

Solution:

Slices of cake eaten by Vanessa = $2$

Slices of cake eaten by Ishan = $1$

Slices remaining = $1$

Total number of Slices = $\text{Slices of cake eaten by Vanessa}+\text{Slices of cake eaten by Ishan}+\text{Slices remaining}$

= $2+1+1$

= $4$

Total number of Slices Eaten = $\text{Slices of cake eaten by Vanessa}+\text{Slices of cake eaten by Ishan}$

= $2+1$

= $3$

Fraction of Slice eaten = $\frac{\text{Total number of slices eaten}}{\text{Total number of slice}}$

= $(3)/(4)$

Therefore the fraction of slice eaten is $(3)/(4)$

so 2 ate by Vanessa + 1 slice ate by Ishaan make 3 + 1 slice reaining so total was 4 slices
and from this result that was eaten 3 slices so this mean that this is a 3/4 part eaten

hope this will help you

Which is equivalent to (4xy – 3z)2, and what type of special product is it?16x2y2 + 9z2, the difference of squares
16x2y2 + 9z2, a perfect square trinomial
16x2y2 – 24xyz + 9z2, the difference of squares
16x2y2 – 24xyz + 9z2, a perfect square trinomial

Answers

(4xy - 3z)²

(4xy - 3z)(4xy - 3z)
4xy(4xy - 3z) - 3z(4xy - 3z)
16x²y² - 12xyz -12xyz + 9z²

16x²y² - 24xyz + 9z², a perfect square trinomial.

The correct option is $\boxed{{\mathbf{Option D}}}$ .

Further explanation:

The binomial algebraic expression is an algebraic expression that consists two terms and it is separated by plus or minus.

Binomial expression can be mathematically expressed as,

$a + b$

The trinomial algebraic expression is an algebraic expression that consists three terms and it is separated by plus or minus.

Trinomial expression can be mathematically expressed as,

$a + b + c$

Here, $a,b{\text{ and }}c$ are the real numbers.

The square of the binomial $a + b$ can be written as,

${\left( {a + b} \right)^2} = \left( {a + b} \right)\left( {a + b} \right)$

Given:

The given algebraic expression is ${\left( {4xy - 3z} \right)^2}$ .

Step by step explanation:

Step 1:

The square of the binomial $a + b$ can be written as,

${\left( {a + b} \right)^2} = \left( {a + b} \right)\left( {a + b} \right)$

Similarly, the expression ${\left( {4xy - 3z} \right)^2}$ can be written as,

$\begin{aligned}{\left( {4xy - 3z} \right)^2} &= \left( {4xy - 3z} \right)\left( {4xy - 3z} \right) \n&= 4xy\left( {4xy - 3z} \right) - 3z\left( {4xy - 3z} \right) \n\end{aligned}$

Step 2:

The distributive property can be used to solve the square of the binomial.

The distributive property can be expressed as,

$a\left( {b + c} \right) = ab + ac$

Now apply the distributive property to solve the expression ${\left( {4xy - 3z} \right)^2}$ .

$\begin{aligned}{\left( {4xy - 3z} \right)^2} &= 4xy\left( {4xy - 3z} \right) - 3z\left( {4xy - 3z} \right) \n&= 16{x^2}{y^2} - 12xyz - 12xyz + 9{z^2} \n&= 16{x^2}{y^2} - 24xyz + 9{z^2} \n\end{aligned}$

Therefore, the expression $16{x^2}{y^2} - 24xyz + 9{z^2}$ is the perfect square of the binomial $\left( {4xy - 3z} \right)$ .

The expression $16{x^2}{y^2} - 24xyz + 9{z^2}$ is the trinomial.

Thus, option D a perfect square trinomial $16{x^2}{y^2} - 24xyz + 9{z^2}$ is correct.

Learn more:

Learn more about the function is graphed below brainly.com/question/9590016
Learn more about the symmetry for a function brainly.com/question/1286775
Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Algebraic expression

Keywords: binomial, polynomial, algebraic expression, difference, product, trinomial, distributive property, equivalent, expression, terms, plus, separated, multiply, minus, addition

Factor the variable expression: 36x + 8y Group of answer choices 4x(9+2) 4(9x+2y) 9(4x+2y) 8(x+2y)

a=13 c=15 A=53 Two sides and an angle​ (SSA) of a triangle are given. Determine whether the given measurements produce one​ triangle, two​ triangles, or no triangle at all. Solve each triangle that results.

Answers

Related Questions

Answers

Answers

Answers

a=13 c=15 A=53 Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results.