MCF3M CPT Part 1 - Chapters 5,7,8 1. In Delta ABC:angle B=90^circ ,angle C=33^circ ,b=4.9cm Draw a sketch of the triangle and solve for all side lengths and angles.

Here's how to solve the triangle:<br /><br />**1. Sketch the Triangle:**<br /><br />Draw a right-angled triangle. Label the right angle as B. Label angle C as 33°. Label the hypotenuse (opposite the right angle) as 'b' and indicate its length as 4.9 cm. Label the side opposite angle A as 'a' and the side opposite angle C as 'c'.<br /><br />**2. Find Angle A:**<br /><br />Since the sum of angles in a triangle is 180°, we have:<br /><br />A + B + C = 180°<br />A + 90° + 33° = 180°<br />A = 180° - 90° - 33°<br />A = 57°<br /><br />**3. Find side 'c' (adjacent to angle C):**<br /><br />We can use the cosine ratio:<br /><br />cos(C) = adjacent/hypotenuse<br />cos(33°) = c/4.9 cm<br />c = 4.9 cm * cos(33°)<br />c ≈ 4.1 cm (rounded to one decimal place)<br /><br />**4. Find side 'a' (opposite angle A):**<br /><br />We can use the sine ratio:<br /><br />sin(C) = opposite/hypotenuse<br />sin(33°) = a/4.9 cm<br />a = 4.9 cm * sin(33°)<br />a ≈ 2.7 cm (rounded to one decimal place)<br /><br /><br />**Solution Summary:**<br /><br />* Angle A = 57°<br />* Angle B = 90°<br />* Angle C = 33°<br />* Side a ≈ 2.7 cm<br />* Side b = 4.9 cm<br />* Side c ≈ 4.1 cm<br />