Solve △ABC using the given measurements. Round measures of sides to the nearest tenth and measures of angles to the nearest degree.
1.) a=7, A=49 degrees,
2.) A=22 degrees,c=8
3.) a=7, c=16
To solve the triangle △ABC, we can use the Law of Sines and the Law of Cosines. Let's go through each given measurement and solve the triangle:
1.) a = 7, A = 49 degrees:
First, using the given angle A and side a, we can use the Law of Sines to find side B:
sin(B) / b = sin(A) / a
sin(B) / b = sin(49°) / 7
sin(B) = (b * sin(49°)) / 7
Next, we can subtract angle A (49 degrees) and angle B from 180 degrees to find angle C:
C = 180° - A - B
Using the Law of Sines again, we can find side C:
sin(C) / c = sin(A) / a
sin(C) / c = sin(49°) / 7
sin(C) = (c * sin(49°)) / 7
Now, we can use the Law of Cosines to find side b:
b^2 = a^2 + c^2 - 2ac * cos(B)
b^2 = 7^2 + c^2 - 2(7)(c) * cos(B)
Finally, we can calculate the values:
- Calculate sin(B) and sin(C) using the sinus function.
- Calculate angle C using 180 - angle A - angle B.
- Calculate side b using the Law of Cosines.
2.) A = 22 degrees, c = 8:
Using the same process as in the first example:
- Calculate angle B using the Law of Sines.
- Calculate angle C using 180 - angle A - angle B.
- Calculate side a using the Law of Sines.
3.) a = 7, c = 16:
Using the same process as before:
- Calculate angle B using the Law of Sines.
- Calculate angle C using 180 - angle A - angle B.
- Calculate side b using the Law of Sines.
Remember to round the measures of sides to the nearest tenth and measures of angles to the nearest degree as specified.
For each question, there are only 2 pieces of independent information,
you need 3.
Did you perhaps forget to mention that the triangles are right-angled?