A man 1.5m tall, observes a bird at the top of a tree 4.5m high. If the bird is 8m away from the man. Calculate the distance between the feet of the man and the base of the tree.

Welcome back adejinledemolae — missed you this week. Here are the solutions to your questions: 1. A man 1.5m tall, observes a bird at the top of a tree 4.5m high. If the bird is 8m away from the man. Calculate the distance between the feet of the man and the base of the tree. Step 1: Determine the effective height difference. The effective height is the height of the tree minus the height of the man. H_eff = 4.5\, m - 1.5\, m = 3\, m Step 2: Use the Pythagorean theorem. Let x be the horizontal distance between the man and the tree. The line of sight to the bird forms the hypotenuse of a right-angled triangle. x^2 + H_eff^2 = (distance to bird)^2 x^2 + (3\, m)^2 = (8\, m)^2 x^2 + 9\, m^2 = 64\, m^2 Step 3: Solve for x. x^2 = 64\, m^2 - 9\, m^2 x^2 = 55\, m^2 x = sqrt(55)\, m x ≈ 7.416\, m The distance between the feet of the man and the base of the tree is approximately 7.416 m. 2. The angle of elevation of a bird in the air from a hunter standing on the ground is 35^. If the bird is 81.7m away along the hunter's line of sight, how high is the bird from the ground? Correct to 1 decimal place. Step 1: Identify the trigonometric relationship. We have the angle of elevation ( = 35^) and the hypotenuse (line of sight distance, d = 81.7 m). We need to find the height (h), which is the opposite side. () = oppositehypotenuse (35^) = (h)/(81.7\, m) Step 2: Solve for h. h = 81.7\, m × (35^) h = 81.7\, m × 0.573576 h ≈ 46.868\, m Step 3: Round to one decimal place. h ≈ 46.9\, m The height of the bird from the ground is approximately 46.9 m. 3. The angle of elevation of the top of a fence from a boy 1.2m tall is 57^. If the boy is 2.4m away from the fence, correct to 2 decimal places, the height of the fence. Step 1: Determine the height of the fence above the boy's eye level. Let H_eff be the height of the fence above the boy's eye level. We have the angle of elevation ( = 57^) and the adjacent side (distance to fence, d = 2.4 m). () = oppositeadjacent (57^) = H_eff2.4\, m H_eff = 2.4\, m × (57^) H_eff = 2.4\, m × 1.53986 H_eff ≈ 3.69566\, m Step 2: Calculate the total height of the fence. The total height of the fence (H_fence) is the height above the boy's eye level plus the boy's height. H_fence = H_eff + 1.2\, m H_fence = 3.69566\, m + 1.2\, m H_fence = 4.89566\, m Step 3: Round to two decimal places. H_fence ≈ 4.90\, m The height of the fence is approximately 4.90 m. 4. The angle of elevation of an aircraft from a point on the horizontal ground is 30^. If the aircraft is 100m above the ground, how far is it from the point? Step 1: Identify the trigonometric relationship. We have the angle of elevation ( = 30^) and the opposite side (height of aircraft, h = 100 m). We need to find the direct distance from the point to the aircraft (line of sight, d_sight), which is the hypotenuse. () = oppositehypotenuse (30^) = 100\, md_sight Step 2: Solve for d_sight. d_sight = 100\, m(30^) d_sight = 100\, m0.5 d_sight = 200\, m The aircraft is 200 m from the point. 5. The angle of elevation of the top of a communication mast from a point is 60^. If the mast is 120m high, how far is the point A from the foot of the mast? Correct to 1 decimal place. Step 1: Identify the trigonometric relationship. We have the angle of elevation ( = 60^) and the opposite side (height of mast, h = 120 m). We need to find the horizontal distance (x) from point A to the foot of the mast, which is the adjacent side. () = oppositeadjacent (60^) = 120\, mx Step 2: Solve for x. x = 120\, m(60^) x = 120\, msqrt(3) x = 120\, m1.73205 x ≈ 69.282\, m Step 3: Round to one decimal place. x ≈ 69.3\, m The point A is approximately 69.3 m from the foot of the mast. Send me the next one 📸