MATHEMATICS MIDDLE SCHOOL

In △ABC, m∠A=72°, c=61, and m∠B=16°. Find the perimeter of the triangle.

Answers

Answer 1

Answer:

The perimeter of the triangle is about 136

Further explanation

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

There are several trigonometric identities that need to be recalled, i.e.

$cosec ~ A = (1)/(sin ~ A)$

$sec ~ A = (1)/(cos ~ A)$

$cot ~ A = (1)/(tan ~ A)$

$tan ~ A = (sin ~ A)/(cos ~ A)$

Let us now tackle the problem!

This problem is about Sine Rule.

First of all, we will calculate the ∠C :

∠A + ∠B + ∠C = 180°

72° + 16° + ∠C = 180°

∠C = 180° - 72° - 16°

∠C = 92°

Next, we will use the Sine Rule to find the length of the other side of the triangle.

$(c)/(\sin \angle C) = (b)/(\sin \angle B)$

$(61)/(\sin 92^o) = (b)/(\sin 16^o)$

$b \approx \boxed {16.82}$

$(c)/(\sin \angle C) = (a)/(\sin \angle A)$

$(61)/(\sin 92^o) = (a)/(\sin 72^o)$

$a \approx \boxed {58.05}$

Finally, we can find the perimeter of a triangle with the following formula

$\text{Perimeter of the triangle} = a + b + c$

$\text{Perimeter of the triangle} = 58.05 + 16.82 + 61$

$\text{Perimeter of the triangle} \approx \boxed {136}$

Learn more

Calculate Angle in Triangle : brainly.com/question/12438587
Periodic Functions and Trigonometry : brainly.com/question/9718382
Trigonometry Formula : brainly.com/question/12668178

Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse

Answer 2

Answer:

Answer:

136

Step-by-step explanation:

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Use distributive property to find 54x8
What is the value of 3 in 3,538
What is 11.7% rounded to the nearest tenth of a percent?

Compare 8 ⋅ 107 to 2 ⋅ 104choice of answers are:
A) 8 ⋅ 107 is 4,000 times larger than 2 ⋅ 104.
B) 8 ⋅ 107 is 400 times larger than 2 ⋅ 104
C) 8 ⋅ 107 is 40 times larger than 2 ⋅ 104.
D)8 ⋅ 107 is 4 times larger than 2 ⋅ 104.

Answers

From what I did none of those answer choices would work.

Answer If divided its 4000

A city manager made a scatter plot of number of retail stores in a certain cirty over years. The scatterplot had a trend like with an equation of y=11x+12, where y is the total number of retail stores and X is the number of years since 1990. Mark and his family moved to a city in 1997. How many retail stores were their in 1997

Answers

Answer: There were 89 retail stores in 1997.

Step-by-step explanation:

Hi, to answer this question, first, we have to calculate the number of years since 1990(x).

1997-1990 = 7 years

Now, we simply substitute x=7 (years) in the equation given

y=11x+12

y=11(7)+12

y=77+12

y = 89 retail stores

There were 89 retail stores in 1997.

Feel free to ask for more if needed or if you did not understand something.

A parallelogram with a base four times the height and an area less than 200 square feet

Answers

The area of a parallelogram is base multiplied by the height.
A parallelogram with a base four times the height and an area less than 200 square feet
B = 4H
Area < 200 square feet.

200 > B*H
200 > 4H * H
200 > 4H^2
50 > H^2
H ~ 5 square root of 2

Answer:196 square ft

Step-by-step explanation:.......................

What is the approximate volume of a cone with a height of 9 ft and radius of 3 ft?Use 3.14 to approximate pi, and express your final answer to the nearest tenth.

?? ft^3

Answers

volume of a cone=1/3 times height times area of base
area of base=area of circle=pi times r^2
r=3
aprox pi to 3.14
height=9

so we have
volume=1/3 times 9 times 3.14 times 3^2
3^2=9
1/3 times 9 times 3.14 times 9
3 times 3.14 time s9
9.42 times 9
84.78
nearest tenth
0.78=0.8

answer is 84.8 ft^3

Answer:wrong

Step-by-step explanation:

A test has 20 questions worth 100 points. The test consists of true/false questionsworth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test? A. 10 mc, 10 t&f
B. 7 mc, 13 t&f
C. 2 mc, 18 t&f
D. 5 mc, 15 t&f

Answers

answer is D) 5 mc, 15 t&f
you have two unknown variables, thus you need two equations

definitions:
a = quantity of multiple choice questions
b = quantity of true and false questions

100 points = a*11 points/question + b*3 points/question
20 questions = a +b

using 2nd equation, find equation for 'a':
a = 20 - b

substitute this equation for 'a' into 1st equation:
100 = 11a + 3b
100 = 11(20 - b) + 3b
100 = 220 - 11b + 3b
100 - 220 = -8b
-120 = -8b
-120/-8 = b
15 = b

resolve 2nd equation now knowing value of 'b':
a = 20 - b
a = 20 - 15
a = 5

verify solution is correct by substituting values into first equation
11a + 3b = 100
11(5) + 3(15) = 100
55 + 45 = 100
100 = 100 [OK]

verify solution is correct by substituting values into second equation
a + b = 20
5 + 15 = 20
20 = 20 [OK]

Final answer:

There are 5 multiple-choice questions on the test.

Explanation:

The total number of points for the test is 100. Let's assume there are x multiple-choice questions on the test. Each multiple-choice question is worth 11 points. So the total number of points for multiple choice questions is 11x. The remaining points, 100 - 11x, are for the true/false questions, each worth 3 points. To find the number of multiple-choice questions, we need to solve the equation: 11x + 3(20 - x) = 100.

Simplifying the equation gives us: 11x + 60 - 3x = 100. Combining like terms gives us: 8x + 60 = 100. Subtracting 60 from both sides gives us: 8x = 40. Dividing both sides by 8 gives us: x = 5.

Therefore, there are 5 multiple-choice questions on the test.