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