Use the Sine Rule.

Here are the solutions to the questions: 37. In a triangle, if a = 10 cm, A = 30^, and B = 60^, find b. Step 1: Use the Sine Rule. The Sine Rule states that for a triangle with sides a, b, c and opposite angles A, B, C: (a)/( A) = (b)/( B) = (c)/( C) Step 2: Substitute the given values into the Sine Rule. 10 cm 30^ = (b)/( 60^) Step 3: Solve for b. We know that 30^ = 0.5 and 60^ = sqrt(3)2 ≈ 0.866. (10)/(0.5) = (b)/(0.866) 20 = (b)/(0.866) b = 20 × 0.866 b = 17.32 cm Step 4: Compare with the given options. The calculated value 17.32 cm is closest to option B. The final answer is B. 17.3 cm. 38. Which formula is the cosine rule? The Cosine Rule relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides a, b, c and angle A opposite side a, the formula is: a^2 = b^2 + c^2 - 2bc A Comparing this with the given options: A. a^2 = b^2 + c^2 is the Pythagorean theorem. B. a^2 = b^2 + c^2 - 2bc A is the Cosine Rule. C. a/ A = b/ B is the Sine Rule. D. A = opposite/adjacent is a trigonometric ratio for right-angled triangles. The final answer is B. a^2 = b^2 + c^2 - 2bc A. 39. A ladder 5 m long leans against a wall, forming a 60^ angle with the ground. What is the height the ladder reaches on the wall? Step 1: Identify the components of the right-angled triangle formed. The ladder is the hypotenuse (H = 5 m). The angle with the ground is = 60^. The height the ladder reaches on the wall is the side opposite to the angle (Opposite = h). Step 2: Use the sine function. The sine function relates the opposite side, hypotenuse, and angle: = OppositeHypotenuse Step 3: Substitute the values and solve for h. 60^ = (h)/(5 m) h = 5 m × 60^ We know that 60^ = sqrt(3)2 ≈ 0.866. h = 5 m × 0.866 h = 4.33 m Step 4: Compare with the given options. The calculated value 4.33 m is closest to option C. The final answer is C. 4.3 m. 40. A man sees the top of a building, an angle of elevation of 30^. He is standing 20 m from the foot of the building. What is the height of the building? Step 1: Identify the components of the right-angled triangle formed. The distance from the building is the adjacent side (Adjacent = 20 m). The angle of elevation is = 30^. The height of the building is the side opposite to the angle (Opposite = h). Step 2: Use the tangent function. The tangent function relates the opposite side, adjacent side, and angle: = OppositeAdjacent Step 3: Substitute the values and solve for h. 30^ = (h)/(20 m) h = 20 m × 30^ We know that 30^ = (1)/(sqrt(3)) ≈ 0.577. h = 20 m × 0.577 h = 11.54 m Step 4: Compare with the given options. The calculated value 11.54 m is closest to option C. The final answer is C. 11.5 m. Send me the next one 📸