List the sides of triangle ΔMNP in ascending order (shortest to longest) if:
m∠M = 64°, m∠N = 48°,
for this one i am not sure if your supposed to find the third angle and or the third side can you guys explain and show me the answer i got 132 degrees but can't find out he side cause i think that u can make the sides as long or short as you want with the same angles
pm, np, mn
Mlb
Ah, triangles can be quite mysterious, but fear not, I shall attempt to shed some light on this for you! In a triangle, the sum of the angles always adds up to 180 degrees. So to find the measure of the third angle in triangle ΔMNP, we can use this nifty formula:
Third Angle = 180 - (Angle M + Angle N)
Plugging in the given values, we have:
Third Angle = 180 - (64 + 48) = 180 - 112 = 68 degrees
Now, for the sides of the triangle, we don't have enough information to determine their exact lengths. Given two angles, we can determine the ratios of the sides using trigonometric functions like sine, cosine, and tangent. However, to find the actual side lengths, you would need more information, such as the length of one side or the length of the altitude.
So unfortunately, without further info, we can't determine the exact lengths of the sides of triangle ΔMNP. It's like trying to juggle invisible objects! But don't worry, there are infinitely many possibilities for the side lengths that will satisfy the given angle measures. Triangles can be quite flexible, just like a good yoga instructor!
To determine the sides of triangle ΔMNP in ascending order, you need to use the information provided about the angles.
In a triangle, the sum of the angles is always 180 degrees. So, to determine the measure of the third angle, you can subtract the sum of the given angles (64° + 48°) from 180°:
180° - (64° + 48°) = 68°
Now that you have found the measure of the third angle (68°), you can proceed to determine the sides of the triangle.
In a triangle, the longest side is always opposite the largest angle, while the shortest side is opposite the smallest angle. In this case, the angles provided are 64° and 48°, so you can determine the longest and shortest sides accordingly.
Therefore, the sides of triangle ΔMNP will be listed in ascending order as follows:
1. The shortest side (opposite the smallest angle of 48°)
2. The second shortest side (opposite the second smallest angle of 64°)
3. The longest side (opposite the largest angle of 68°)
Please note that without specific measurements or additional information about the side lengths, you cannot determine the exact lengths of the sides.
pm, mp, mn
First of all your third angle is 68° , not 132°
You are not asked to state the lengths of the sides, simply list them in order of size.
The property to use is: In any triangle , the longest side is opposite the largest angle, the smallest side is opposite the smallest angle, ...
so N is the smallest angle,
M is the midsize angle, and
P is 68°, making its opposite side as the largest.
So list them