How many triangles does a=6 b=10 A=33° create?

2 triangles are possible.

Step-by-step explanation:

Given

a=6

b=10

A=33°

To find:

Number of triangles possible ?

Solution:

First of all, let us use the sine rule:

As per Sine Rule:

And let us find the angle B.

This value is in the 1st quadrant i.e. acute angle.

One more value for B is possible in the 2nd quadrant i.e. obtuse angle which is: 180 - 65.44 =

For the value of , let us find :

Let us find side c using sine rule again:

So, one possible triangle is:

a = 6, b = 10, c = 10.89

A=33°, A=65.44°, C=81.56°

For the value of , let us find :

Let us find side c using sine rule again:

So, second possible triangle is:

a = 6, b = 10, c = 5.91

A=33°, A=114.56°, C=32.44°

So, answer is : 2 triangles are possible.

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

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step-by-step explanation: