Question

Given: △ABC, m∠A=60°,

Answer 1

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Answer 2

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 $AB = 9$

Calculation:

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

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

The sine rule in triangle ABC can be expressed as,

$\begin{aligned}\frac{{BC}}{{\sin {{60}^\circ }}} &= \frac{9}{{\sin {{45}^\circ }}} \\BC&= \frac{9}{{\frac{1}{{\sqrt2 }}}} \times \frac{{\sqrt 3 }}{2}\\BC &= 11.02\\\end{aligned}$

The length of AC can be calculated as follows,

$\begin{aligned}\frac{{AB}}{{\sin {{45}^\circ }}}&= \frac{{AC}}{{\sin {{75}^\circ }}}\\\frac{9}{{\sin {{45}^\circ }}} \times \sin {75^\circ } &= AC\\12.30&= AC\\\end{aligned}$

The perimeter of triangle ABC can be obtained as follows,

$\begin{aligned}{\text{Perimeter}} &= AB + BC + AC \\ &= 9 + 11.02 + 12.30\\&= 32.32\\\end{aligned}$

The area of triangle ABC can be obtained as follows,

$\begin{aligned}{\text{Area}} &= \frac{1}{2} \times AB \times AC \times \sin \left( A \right)\\&= \frac{1}{2} \times 9 \times 12.30 \times \sin {60^\circ }\\&= 4.5 \times 12.30 \times \frac{{\sqrt3 }}{2}\\&= 47.93\\\end{aligned}$

The perimeter of triangle of ABC is $\boxed{32.32}$ and the area of triangle ABC is $\boxed{47.93}.$

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.