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
Dima020 [189]
4 years ago
5

Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC

Mathematics
2 answers:
jarptica [38.1K]4 years ago
6 0

We are given

△ABC, m∠A=60° m∠C=45°, AB=8

Firstly, we will find all angles and sides

Calculation of angle B:

we know that sum of all angles is 180

m∠A+ m∠B+m∠C=180

we can plug values

60°+ m∠B+45°=180

m∠B=75°

Calculation of BC:

we can use law of sines

\frac{AB}{sin(C)}=\frac{BC}{sin(A)}

now, we can plug values

\frac{8}{sin(45)}=\frac{BC}{sin(60)}

BC=\frac{8}{sin(45)} \times sin(60)

BC=9.798

Calculation of AC:

\frac{AB}{sin(C)}=\frac{AC}{sin(B)}

now, we can plug values

\frac{8}{sin(45)}=\frac{AC}{sin(75)}

AC=\frac{8}{sin(45)} \times sin(75)

AC=10.928

Perimeter:

p=AB+BC+AC

we can plug values

p=10.928+8+9.798

p=28.726

Area:

we can use formula

A=\frac{1}{2}AB \times AC \times sin(A)

now, we can plug values

A=\frac{1}{2}8 \times 10.928 \times sin(60)

A=37.85570...............Answer

igomit [66]4 years ago
6 0

The perimeter of triangle of ABC is \boxed{28.73}.

Further explanation:

Given:

The measure of angle A is \angle A = {60^ \circ }.

The measure of angle C is \angle C = {45^ \circ }.

The length of side AB is AB = 8

Calculation:

The sum of all angles of a triangle is {180^ \circ }.

\begin{aligned}\angle A + \angle B + \angle C&={180^ \circ }\\{60^ \circ } + \angle B + {45^ \circ }&= {180^ \circ }\\{105^ \circ }+\angle B&= {180^ \circ }\\\angleB&= {180^ \circ } - {105^ \circ }\\\angleB&= {75^ \circ }\\\end{aligned}

The sine rule in triangle ABC can be expressed as,

\begin{aligned}\frac{{BC}}{{\sin {{60}^ \circ }}}&=\frac{8}{{\sin {{45}^ \circ }}}\\BC&= \frac{8}{{\frac{1}{{\sqrt2 }}}} \times \frac{{\sqrt 3 }}{2}\\BC &= 9.80\\\end{aligned}

The length of AC can be calculated as follows,

\begin{aligned}\frac{{AB}}{{\sin {{45}^ \circ }}}&=\frac{{AC}}{{\sin {{75}^ \circ }}}\\\frac{8}{{\sin {{45}^ \circ }}}\times \sin {75^ \circ }&= AC\\10.93& = AC\\\end{aligned}

The perimeter of triangle ABC can be obtained as follows,

\begin{aligned}{\text{Perimeter}}&= AB + BC + AC\\&= 8 + 9.80 + 10.93\\&= 28.73\\\end{aligned}

The area of triangle ABC can be obtained as follows,

\begin{aligned}{\text{Area}}&=\frac{1}{2} \times AB \times AC \times \sin \left( A \right)\\&= \frac{1}{2}\times 8 \times 10.93 \times \sin {60^ \circ }\\&= 4\times 10.93 \times \frac{{\sqrt3 }}{2}\\&= 37.86\\\end{aligned}

The perimeter of triangle of ABC is \boxed{28.73} and the area of triangle ABC is \boxed{37.86}.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: angles, ABC, angle A=60 degree, perimeter, area of triangle, triangle ABC.

You might be interested in
Can someone also help me with this please and thankss
VMariaS [17]

Answer: The measure of angle 3 is 50 degrees.

Step-by-step explanation:

We know that angle 2 is 130 degrees.

Angle 1 and angle 2 are verticle angles which means that they are across and equal to each other.

So angle 1 and angle 2 are 130 degrees.

Add up both angle 1 and angle 2, 130 + 130 = 260.

Now, all of these angles add up to be 360 degrees in total as they make a circle and there are 360 degrees in one.

Subtract 260 from 360, 360 - 260 = 100.

Since both angle 3 and angle 4 are also verticle angles we need to split the 100 degrees evenly, 100 ÷ 2 = 50.

So, angle 3 is 50 degrees.

8 0
3 years ago
Read 2 more answers
Four cups are placed upturned on the counter. each cup has the same number of sweets and a declaration about the number of sweet
Mumz [18]

Answer:

6?    i hope this helps some!   :)

Step-by-step explanation:

each has 6 in between the number

5 or 6 p there is a possibility of there being 6

7 or 8 there is at least 6 in this cup

6 or 7 there is at least 6 in this cup

7 or 5 there is a possibility of there being 6

4 0
3 years ago
Which algebraic properties was applied to the expression a + (b + c) = (a + b) + c?
andrew11 [14]

Answer:

the Associative Property

Step-by-step explanation:

Notice that the ORDER doesn't change -- a, b, c on both sides.  But the GROUPING changes.

Example:

3 + (4 + 5) = (3 + 4) + 5

3 + 9 = 7 + 5

12 = 12

Subtraction does NOT behave this way!

8 - (7 - 1) = 8 - 6 = 2

(8 - 7) - 1 = 1 - 1 = 0

It matters who you associate with!  :-)

5 0
3 years ago
Derive the equation of the parabola with a focus at (–5, 5) and a directrix of y = -1.
Elza [17]
( x + 5 )^2 = - ( y - 5 )
6 0
3 years ago
Read 2 more answers
Directions: Read, analyze, and choose the letter of the correct answer. Write your
svetoff [14.1K]

1) The normal room temperature is said to be about 20°C

2) 5 day is equivalent to 120 hr

3) 756 m³/s is equivalent 56000 L/s

4) It would take the snail 5 hours to crawl 75 m

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

1) The normal room temperature is said to be about 20°C

2) 1 day = 24 hr

5 day = 5 day * 24 hr per day = 120 hr

3) 1 m³ = 1000 L

756 m³/s = 56 m³/s * 1000 L/m³ = 56000 L/s

4) 1 m = 100 cm

75 m = 7500 cm

Time = 7500 / (25 cm/min) = 300 min = 5 hours

Find out more on equation at: brainly.com/question/2972832

#SPJ1

6 0
2 years ago
Other questions:
  • What two theories can be used to predict molecular geometry?
    9·1 answer
  • Which data outcome of the number of customers in line would best support opening another cash register?
    13·1 answer
  • Mt Whitney is 4392m at its highest point. Bombay Beach, California, is 86 m below sea level (-86). What is the difference betwee
    14·1 answer
  • Determine whether the relation is a function. (1-4), (2, 1), (3, 4), (3, 3). (4, 2)
    14·1 answer
  • May i get help with 5-9 questions pls
    8·1 answer
  • II. Write whether each number is an EXPRESSION or an EQUATION.
    9·1 answer
  • HELP ASAP PLS!! An explanation too pls
    12·1 answer
  • Seth needs to buy mulch to cover a circular garden. The garden has a radius of 5ft. Mulch costs $0.25 per square foot. How much
    12·1 answer
  • Pls help!!<br> 94 + 8r - 7
    5·2 answers
  • Simplify (9x^3+2x^2-5x+4)-(5x^3-7x+4)
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!