The right triangle which right angle is at P and PR is parallel to the x-axis can have 4 sets (A,B,C,D as illustrated) of format depends on which direction is the right angle located.
each set have
(1+2+3+4+5+6+7+8+9) x (1+2+3+4+5+6+7+8+9+10) = 45 x 55 = 2475 right triangles
4 sets: 2475 x 4 = 9900
As we can observe from the drawing that with increasing length of side C the angle C also increases.
For tingle #1
We can find angle C using the triangle sum theorem: the three interior angles of any triangle add up to 180 degrees. Since we know the measures of angles A and B, we can find C.
We cannot find any of the sides. Since there is noting to show us size, there is simply just not enough information; we need at least one side to use the rule of sines and find the other ones. Also, since there is nothing showing us size, each side can have more than one value.
For triangle #2
In this one, we can find everything and there is one one value for each.
- We can find side c
Since we have a right triangle, we can find side c using the Pythagorean theorem
- We can find angle C using the cosine trig identity
- Now we can find angle A using the triangle sum theorem
For triangle #3
Again, we can find everything and there is one one value for each.
- We can find angle A using the triangle sum theorem
- We can find side a using the tangent trig identity
- Now we can find side b using the Pythagorean theorem
I cannot draw on this. How do I enter my answer?
we are given with two sides of a triangle. the given sides are a=2cm, b=5cm.
we have been asked to draw four different triangles with the given two side lengths.
as we know from the tringular inequality that
the sum of the length of any two sides should be greater than the length of the third side.
using this concept let the length of the third side be
the drawing has been attched.
as we can observe from the drawing that with increasing length of side c the angle c also increases.
A triangle with angle 23°, 54° and 103° is a defined triangle, because the sum of angle in a triangle is 180°.
So the triangle is defined.
But, the angle 23°, 54° and 130° is ambiguously defined beause no length was mention. It is possible to draw many other similar triangles with those angles. So any other triangle he constructs with those angles will be similar to the original triangles.
Hoped I helped!
If the assumed length of c is less than 7, a triangle will not be formed.