A vertical post TF stands on level ground. The angle of depression from T to B is 25 degrees and from T to A is 18 degrees. B and A are on the ground such that F, B, A are collinear and B is between F

You're on a roll — here are the solutions to the questions: 17. a) Let T be the top of the post and F be the foot of the post. Let H be the height of the post. Points A and B are on the ground, on the same line as the foot of the post. Point B is nearer to the foot of the post (F) than point A. The angle of depression from T to B is 25^. The angle of depression from T to A is 18^. The distance between A and B is 70 m. Here is a sketch representing the positions: ` T (Top of post) | \ | \ | \ | \ | \ H | \ | \ | \ | \ F-------------------B-------------------A <---- x ----><----- 70m -----> ` In the sketch: • TF is the height of the post, H. • F is the foot of the post. • B is a point on the ground, closer to F. • A is a point on the ground, further from F. • TBF = 25^ (angle of elevation from B to T, which is equal to the angle of depression from T to B). • TAF = 18^ (angle of elevation from A to T, which is equal to the angle of depression from T to A). • Distance FB = x. • Distance AB = 70 m. • Distance FA = x + 70 m. b) i) The height of the post from the ground level. Step 1: Set up trigonometric equations for the two right-angled triangles, TFB and TFA. In TFB: (25^) = (TF)/(FB) = (H)/(x) So, H = x (25^) (Equation 1) In TFA: (18^) = (TF)/(FA) = (H)/(x + 70) So, H = (x + 70) (18^) (Equation 2) Step 2: Equate the expressions for H to solve for x. x (25^) = (x + 70) (18^) x (25^) = x (18^) + 70 (18^) x (25^) - x (18^) = 70 (18^) x ((25^) - (18^)) = 70 (18^) x = (70 (18^))/((25^) - (18^)) Step 3: Calculate the numerical value of x. Using a calculator: (18^) ≈ 0.324919696 (25^) ≈ 0.466307658 x = (70 × 0.324919696)/(0.466307658 - 0.324919696) x = (22.74437872)/(0.141387962) x ≈ 160.86001 m Step 4: Substitute the value of x back into Equation 1 to find H. H = x (25^) H = 160.86001 × 0.466307658 H ≈ 75.0071 m Step