Question

draw triangle ABC with AB=8cm, BC=6cm, and angle B=30°. Draw a right angled triangle of the same area. Measure it's perpendicular sides. Calculate the area of the triangle.​

Answer 1

Concept:

Triangles are of three types. They are isoceles triangle, right angled angled and equilateral triangle.

Given:

$AB=8cm$ and $BC$ is $6 cm$ and angle $B$ is $30degrees$

Find:

• Draw a triangle $ABC$.
• Draw a right angled traingle of the same area and meaure its perpendicular.
• Calculate the area of traingle.

Solution:

According to the problem,

The traingle is as follows,

Since we need to draw a right angled traingle thus the perpendicular sides will have same length as the length of the triangle.

Let the third unknown side be $AC$

Thus the third side can be found by using law of cosines,

Let $a=6cm$

$c=8cm$

$b=$ unknown side $AC$

Therefore,

$b^2=a^2+c^2-2ac$$cosB$

$=(8)^2+(6)^2-2*8*6cos30$

$=64+36-96*\frac{\sqrt{3} }{2}$

$=100-48\sqrt{3}$

$=100-83.14$

$=16.86$

$=17cm$ approximately

Since we need to draw a right angled traingle thus the perpendicular sides will have same length measure as the length of the triangle $AC$

Thus $AC=17cm$

Area of the triangle is $A=\frac{1}{2}*b*h$

$=\frac{1}{2} *6*17$

$=3*17$

$=51cm$

Hence, the measure of the perpendicular sides is $17cm$ approximately and the area of the triangle is $51cm$.