Determine if there are zero, one, or two triangles for the following: m∠A=48° a=10 m b=12 m

since 10 > 12 sin48° there are two triangles

Well, let's find out if we can make a triangle with the given measurements.

For a triangle to be possible, the sum of any two sides must be greater than the third side. So, let's check if this condition is met.

First, let's check if a + b > c:
10 + 12 = 22, which is greater than the third side c.

Now, let's check if a + c > b:
10 + c > 12
c > 2

Lastly, let's check if b + c > a:
12 + c > 10
c > -2

Since the third side c can't be negative, we can conclude that there is only one possible triangle that can be formed with these given measurements.

So, there is one triangle with m∠A=48°, a=10m, and b=12m. Hope this helps!

To determine the number of triangles that can be formed, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given:
m∠A = 48°
a = 10m
b = 12m

To determine the number of triangles, we need to check the triangle inequality for each combination of sides.

1. Side a and side b:
a + b > c
10 + 12 > c
22 > c

2. Side a and angle A:
a + c > b
10 + c > 12
c > 2

3. Side b and angle A:
b + c > a
12 + c > 10
c > -2

Based on the inequalities above, we can see that side c (unknown side) must be greater than 2 units and less than 22 units.

Therefore, there is only one triangle that can be formed with the given information.

To determine the number of triangles for the given information, we can use 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 third side.

In this case, the information provided is:
m∠A = 48° (angle A measures 48 degrees),
a = 10 (side a measures 10 units),
m b = 12 (measure of side b is 12 units).

Now, let's apply the triangle inequality theorem:
1. Side a + side b > side c
Substitute the given values: 10 + 12 > side c
Simplify: 22 > side c

2. Side b + side c > side a
Substitute the given values: 12 + side c > 10
Simplify: 12 + side c > 10

3. Side c + side a > side b
Substitute the given values: side c + 10 > 12
Simplify: side c + 10 > 12

Now, let's solve these inequalities to determine the number of possible triangles:

1. 22 > side c
This inequality does not provide any specific information about side c, so we cannot determine anything from it.

2. 12 + side c > 10
Subtract 12 from both sides to isolate side c: side c > -2
Since side lengths cannot be negative, this inequality is always true.

3. side c + 10 > 12
Subtract 10 from both sides to isolate side c: side c > 2
This inequality provides information that side c must be greater than 2.

From the inequalities, we see that side c can range from being greater than -2 to being greater than 2. However, since side lengths cannot be negative, we can deduce that side c must be greater than 2.

Therefore, we can conclude that there is only one possible triangle with the given conditions.