In the diagram, a ladder TF, 10 metres long is placed against a wall at an angle of 70° to the horizontal.
(a) How high up the wall, correct to the nearest metre, does the ladder reach?
(b) If the foot (F) of the ladder is pulled from the wall to F\(^{1}\) by 1 metre, (i) how far, correct to 2 significant figures, does the top T slide down the wall to T\(^{1}\).
(ii) Calculate, correct to the nearest degree, \(QF^{1}T^{1}\).
Explanation
(a) \(TQ = 10 \sin 70° = 10 \times 0.9397 = 9.397m\)
\(\approxeq 9m\)
(b)(i) \(QF = 10 \cos 70° = 10 \times 0.3420 = 3.42m\)
\(QF^{1} = 3.42m + 1m = 4.42m\)
\(QT^{1} = \sqrt{10^{2} - 4.42^{2}} = \sqrt{100 - 19.5364}\)
= \(\sqrt{80.4636} = 8.97m\)
\(TT^{1} = 9.397 - 8.97 = 0.43m\)
(ii) \(\sin < QF^{1}T^{1} = \frac{8,97}{10} = 0.897\)
\(< QF^{1} T^{1} = 63.768° \approxeq 64°\)