Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm, calculate correct to the nearest degree, the smallest angle of the triangle.

Answer Details

If two sides of a triangle are perpendicular, then those sides are the legs of a right-angled triangle. We can use Pythagoras' theorem to find the hypotenuse of this right-angled triangle which will be the longest side of the original triangle. Using Pythagoras' theorem: a² + b² = c² where a and b are the lengths of the legs and c is the length of the hypotenuse. In this case, a = 6cm and b = 8cm. So, 6² + 8² = c² 36 + 64 = c² 100 = c² c = 10cm So, the longest side of the triangle is 10cm. Now, we can use trigonometry to find the smallest angle of the triangle. sin A = opposite / hypotenuse where A is the smallest angle of the triangle. We know that the opposite side to A is 6cm (the shorter leg). So, sin A = 6 / 10 sin A = 0.6 Using a calculator or a trigonometric table, we can find the angle whose sine is 0.6. A = 36.87^o (rounded to the nearest degree) Therefore, the smallest angle of the triangle is approximately 37^o. So, the answer is (c) 37^o.