Theory question 108
Inequalities(a) Solve the inequality (1/3)x − (1/4)(x + 2) ≥ 3x − 1⅓.
(b) In the diagram, ABC is right-angled triangle on a horizontal ground. |AD| is a vertical tower. ∠BAC = 90°, ∠ACB = 35°, ∠ABD = 52° and |BC| = 66 m. Find, correct to two decimal places: (i) the height of the tower; (ii) the angle of elevation of the top of the tower from C.
Show the model answer
Model answer
(a) Multiply by 12: 4x − 3(x + 2) ≥ 36x − 16
x − 6 ≥ 36x − 16 → −35x ≥ −10
x ≤ 2/7 (sign flips when dividing by a negative)
(b)(i) |AB| = 66 sin 35° = 37.86 m; |AD| = |AB| tan 52° = 48.45 m
(ii) |AC| = 66 cos 35° = 54.06 m
tan θ = 48.45/54.06 = 0.8962 → θ = 41.87°
Explanation
Find AB and AC in the flat triangle first, then use the vertical triangles.