The angles of triangle ABC are as follows:
Angle A = 37.4°
Angle B = 32.7°
Angle C = 28.9°
Here is a solution to the triangle ABC, where AB = 10 cm, BC = 8 cm, and AC = 7 cm, without using the Pythagorean Theorem:
Since we are not using the Pythagorean Theorem, we will need to use a different method to solve for the angles of the triangle. One way to do this is to use the Law of Cosines.
The Law of Cosines states that:
cos(C) = (a^2 + b^2 - c^2) / (2ab)
where C is the angle opposite side c, and a and b are the other two sides of the triangle.
We can use this formula to solve for the angle C in triangle ABC:
cos(C) = (10^2 + 8^2 - 7^2) / (2 * 10 * 8)
cos(C) = 7 / 8
C = arccos(7 / 8)
C = 28.9°
Now that we know the angle C, we can use the Law of Sines to solve for the other two angles of the triangle.
The Law of Sines states that:
sin(A) / a = sin(B) / b = sin(C) / c
where A and B are the angles opposite sides a and b, respectively.
We can use this formula to solve for the angle A in triangle ABC:
sin(A) / 10 = sin(28.9°) / 7
sin(A) = 0.61
A = arcsin(0.61)
A = 37.4°
We can do the same thing to solve for the angle B:
sin(B) / 8 = sin(28.9°) / 7
sin(B) = 0.53
B = arcsin(0.53)
B = 32.7°
Therefore, the angles of triangle ABC are as follows:
Angle A = 37.4°
Angle B = 32.7°
Angle C = 28.9°
Complete question:
In triangle ABC, where AB = 10 cm, BC = 8 cm, and AC = 7 cm. Find Angles of triangle.