Determine the number of triangles that could be drawn with the given measure. Then, find the measures of the other angles and the other side in each possible triangle. Round side lengths to the nearest tenth of a unit and angle measure to the nearest tenth of a degree, where necessary. a) triangle STU, where angle S=29', s=3.5cm, b=6m. Can you also draw the triangle to help show the values?
Reiny went through this for you once. Now, maybe if you say which side of STU is b, we can make some headway.
sorry it should be corrected to t
To determine the number of triangles that could be drawn with the given measures, we need to apply the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let's analyze the given measurements:
- Angle S = 29'
- Side s = 3.5 cm
- Side b = 6 m
We need to check if the given measurements satisfy the triangle inequality theorem:
s + b > a,
s + a > b,
a + b > s.
Let's calculate the remaining side length, a:
For the first inequality:
3.5 cm + 6 m > a
First, let's convert 6 m to cm by multiplying it by 100:
6 m * 100 cm/m = 600 cm
3.5 cm + 600 cm > a
603.5 cm > a
For the second inequality:
3.5 cm + a > 6 m
Again, convert 6 m to cm:
6 m * 100 cm/m = 600 cm
3.5 cm + a > 600 cm
For the third inequality:
a + 6 m > 3.5 cm
Again, convert 6 m to cm:
6 m * 100 cm/m = 600 cm
a + 600 cm > 3.5 cm
From these calculations, we can see that a must be greater than 603.5 cm, but simultaneously less than 3.5 cm. This is not possible, as a side length cannot be simultaneously longer and shorter than another side.
Therefore, using the given measurements, we cannot form a valid triangle.