Question

Q8) A triangle has sides equal to 6 m, 10 m and 7 m, then the measure of smallest

angles to nearest tenth is:
A) 14.1°
B) 25.7°
C) 36.2°

Answer 1

To find the measure of the smallest angle in a triangle, we can use the Law of Cosines and subtract the sum of the other two angles from 180°.

Step-by-step explanation:

To find the measure of the smallest angle in a triangle, we can use the Law of Cosines. Let's call the sides of the triangle a, b, and c, and the angles opposite these sides A, B, and C respectively. According to the Law of Cosines, we have the formula:

c^2 = a^2 + b^2 - 2ab*cos(C)

In this case, the given sides are 6m, 10m, and 7m. Let's use the formula to find the measure of the smallest angle:

c^2 = 6^2 + 10^2 - 2*6*10*cos(C)

49 = 36 + 100 - 120cos(C)

120cos(C) = -13

cos(C) ≈ -13/120

C ≈ 109.7°

Since the smallest angle is opposite the smallest side, the smallest angle is A. Therefore, to find the measure of the smallest angle, we subtract the sum of the other two angles from 180°:

A ≈ 180° - (B + C)

A ≈ 180° - (x° + 109.7°)

A ≈ 70.3°

Therefore, the measure of the smallest angle to the nearest tenth is 70.3°.

Learn more about Triangle angles