Math, asked by christythomas063, 11 months ago

In triangle ABC, AB = 6 cm, BC = 7cm, ∠B=3 0 . Then a) Draw the triangle ABC. b) Draw a right angled triangle having same area. c) Measure the perpendicular sides d) Find the area of the triangles

Answers

Answered by VarmaGadiraju
4

Answer:

Step-by-step explanation:

• The six elements of a triangle are its three angles and the three

sides.

• The line segment joining a vertex of a triangle to the mid point of its

opposite side is called a median of the triangle. A triangle has

3 medians.

• The perpendicular line segment from a vertex of a triangle to its

opposite side is called an altitude of the triangle. A triangle has

3 altitudes.

• An exterior angle of a triangle is formed, when a side of a triangle is

produced.

• The measure of any exterior angle of a triangle is equal to the sum of

the measures of its two interior opposite angles.

• The sum of the three angles of a triangle is 180°.

• A triangle is said to be equilateral, if each of its sides has the same

length.

• In an equilateral triangle, each angle has measure 60°.

• A triangle is said to be isosceles if at least two of its sides are of same

length.

• The sum of the lengths of any two sides of a triangle is always greater

than the length of the third side

Answered by KajalBarad
1

The required triangle ABC with AB = 6 cm, BC = 7 cm, and angle B (=30\degree degrees) is in the figure-1 (attached here). We cannot draw a right-angled triangle when only its area is given.

Given:

In the triangle ABC, AB = 6 cm, BC = 7 cm, \angleB=30\degree degrees.

To Find:

The area of the triangle ABC and draw it. Draw a right-angled triangle having the same area and measure the perpendicular sides.

Solution:

We shall solve the problem in the following way.

We shall draw the angle B=30\degree degrees, and name the arms of the angle B such that AB = 6 cm, and  BC = 7 cm.

We shall then join the points C and C to form the triangle ABC as shown in the figure-1 (attached here).

We know that the area of a triangle with two known sides a, and b (say), and the known angle X (say) is as follows.

Area=ab\frac{sinX}{2}

We shall find the area of the triangle ABC in the following way.

Area_ABC=(AB)\times (BC)\times \frac{sinB}{2} \\=6\times 7\times \frac{sin30}{2} \\=10.5 cm^{2} (approximate)

We know that to draw the right-angled triangle we need the length of one of its sides as the minimum number of equations required to solve for two variables is two, and here we have two variables with one equation (representing the area) only.

Therefore, the right-angled triangle cannot be drawn by knowing its area only.

Thus the required triangle ABC with AB = 6 cm, BC = 7 cm, and angle B (=30\degree degrees) is in the figure-1 (attached here). We cannot draw a right-angled triangle when only its area is given.

#SPJ3

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