Question

In triangle ABC, AB = 12 cm, A = 30°, B = 60° , = . Find the area of the triangle.
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Answer 1

Answer:

18√3 sq.units (By using trignometric functions and triangle formula =(1/2×b×h).

Answer 2

Answer:

The area of the triangle$18\sqrt{3}\; cm^2$.

Given:

$\angle A=30 \textdegree and \; \angle B=60 \textdegree$

$AB=12cm$

Step-by-step explanation:

$\angle A+ \angle B+ \angle C= 180\textdegree$

$30\textdegree+60\textdegree+\angle C=180\textdegree$

$\angle C= 90\textdegree$

$Cos60\textdegree=\frac{y}{12}\\\frac{1}{2}=\frac{y}{12}\\ 2y=12\\ y=6$

Now,

$Sin 60\textdegree =\frac{x}{12}$

$\frac{\sqrt{5} }{2} =\frac{x}{12}$

$x=\frac{2\sqrt{3} }{2}$

$x=6\sqrt{3}$

$\therefore$ Area of $\triangle ABC= \frac{1}{2} \times l\times b$

$= \frac{1}{2}\times 6\times 6\sqrt{3}$

$= 18\sqrt{3} cm^2$

About triangle:

• The area of a triangle is the region contained by it in a two-dimensional plane. A triangle, as we know, is a closed form with three sides and three vertices. Thus, the area of a triangle is the total space occupied by its three sides. The typical formula for calculating the area of a triangle is half the product of its base and height.

• In general, a "area" is defined as the region inhabited inside the boundaries of a flat object or figure. The measurement is done in square units, with the standard unit being square metres (m2). There are standard formulas for computing area for squares, rectangles, circles, triangles, and so on.

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