Given: △abc, m∠a=60° m∠c=45°, ab=8 find: perimeter of △abc, area of △abc

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

now, we can plug values

Calculation of AC:

now, we can plug values

Perimeter:

we can plug values

Area:

we can use formula

now, we can plug values

...............Answer

The perimeter of triangle of ABC is

Further explanation:

Given:

The measure of angle A is

The measure of angle C is

The length of side AB is

Calculation:

The sum of all angles of a triangle is

The sine rule in triangle ABC can be expressed as,

The length of AC can be calculated as follows,

The perimeter of triangle ABC can be obtained as follows,

The area of triangle ABC can be obtained as follows,

The perimeter of triangle of ABC is and the area of triangle ABC is

Learn more:

1. Learn more about inverse of the function .

2. Learn more about equation of circle .

3. Learn more about range and domain of the function

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

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

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

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