Answer:
The descriptions which can describe more than one triangle is:
- angle measurements of 35°,35° and 110°.
- angle measurements of 40°,60° and 80°.
Step-by-step explanation:
- The three given side lengths form a triangle if the sum of any 2 sides is greater than the length of the third side.
- Also, all the three given angle measure form a triangle if the sum of all the three angles is equal to 180 degree.
- We know that with the help of given side three lengths of a triangle a unique triangle is formed.
- and with the help of given three angle measures of a triangle more than one triangle is possible with distinct side length.
a)
Side lengths 6 ft, 8 ft and 10 ft.
First we check whether it form a triangle or not:
6+8=14>10
8+10=18>6
and
6+10=16>8
Yes, these side lengths form a triangle.
With the help of this only one unique triangle is possible.
b)
angle measurements of 35°,35° and 110°
First we check the sum of the angles:
35°+35°+110°=180°
Hence, more than one triangle is possible.
c)
angle measurements of 30°,40° and 50°
First we check the sum of these angles:
30°+40°+50°=120°≠180°
Hence, these angles measure do not form a triangle.
d)
angle measurements of 40°,60° and 80°
First we check the sum of these angles:
40°+60°+80°=180°.
Hence, more than one triangle is possible.
e)
side length of 4 cm, 6 cm and 9 cm.
First we check whether it form a triangle or not:
4+6=10>9
6+9=15>4
and
4+9=13>6
Hence, a unique triangle will be formed.
