High School Math : Acute / Obtuse Triangles
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Example Questions
Example Question #1 : How To Find The Perimeter Of An Acute / Obtuse Triangle
Two similiar triangles have a ratio of perimeters of 
If the smaller triangle has sides of 3, 7, and 5, what is the perimeter of the larger triangle.
Adding the sides gives a perimeter of 15 for the smaller triangle. Multipying by the given ratio of 
Example Question #1 : Acute / Obtuse Triangles
Two sides of an isosceles triangle are 20 and 30. What is the difference of the largest and the smallest possible perimeters?
15
The answer cannot be determined
0
10
30
10
The trick here is that we don't know which is the repeated side. Our possible triangles are therefore 20 + 20 + 30 = 70 or 30 + 30 + 20 = 80. The difference is therefore 80 – 70 or 10.
Example Question #2 : How To Find The Perimeter Of An Acute / Obtuse Triangle
Two similiar triangles exist where the ratio of perimeters is 4:5 for the smaller to the larger triangle. If the larger triangle has sides of 6, 7, and 12 inches, what is the perimeter, in inches, of the smaller triangle?
18
25
23
20
20
The larger triangle has a perimeter of 25 inches. Therefore, using a 4:5 ratio, the smaller triangle's perimeter will be 20 inches.
Example Question #551 : Geometry
If a = 7 and b = 4, which of the following could be the perimeter of the triangle?
I. 11
II. 15
III. 25
I, II and III
II Only
I and II Only
II and III Only
I Only
II Only
Consider the perimeter of a triangle:
P = a + b + c
Since we know a and b, we can find c.
In I:
11 = 7 + 4 + c
11 = 11 + c
c = 0
Note that if c = 0, the shape is no longer a trial. Thus, we can eliminate I.
In II:
15 = 7 + 4 + c
15 = 11 + c
c = 4.
This is plausible given that the other sides are 7 and 4.
In III:
25 = 7 + 4 + c
25 = 11 + c
c = 14.
It is not possible for one side of a triangle to be greater than the sum of both of the other sides, so eliminate III.
Thus we are left with only II.
Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle
Solve for 
The angles of a triangle must add to 180o. In the triangle to the right, we know one angle and can find another using supplementary angles.
Now we only need to solve for 
Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle
If 
Not enough information to solve
All of the interior angles of a triangle add up to 
If 
Therefore,
Now, 
Also, by definition, the angle of an exterior angle of a triangle is equal to the measure of the two interior angles opposite of it 
Example Question #231 : Geometry
Two interior angles in an obtuse triangle measure 
Interior angles of a triangle always add up to 180 degrees.
Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle
In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?
Since the sum of the angles of a triangle is 
If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.
Example Question #432 : Geometry
Triangle ABC has angle measures as follows:
What is 
90
44
79
57
19
57
The sum of the measures of the angles of a triangle is 180.
Thus we set up the equation
After combining like terms and cancelling, we have
Thus
Example Question #1 : Isosceles Triangles
The base angle of an isosceles triangle is five more than twice the vertex angle. What is the base angle?
Every triangle has 180 degrees. An isosceles triangle has one vertex angle and two congruent base angles.
Let 
So the equation to solve becomes
Thus the vertex angle is 34 and the base angles are 73.
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