5.2.4 Trigonometric Ratios, PT3 Focus Practice


Question 9:
Diagram below shows a vertical pole, PQ. At 2.30 p.m. and 5.00 p.m., the shadow of the pole falls on QR and QS respectively.
Calculate
(a) the height, in m, of the pole.
(b) the value of w.

Solution:
(a)
tan  55 o = Height of the pole 3.2 Height of the pole=tan  55 o ×3.2 =1.428×3.2 =4.57 m

(b)
tan w= 4.57 3.20+2  = 4.57 5.20  =0.879    w= 41 o 18



Question 10:
A technician needs to climb a ladder to repair a street lamp as shown in Diagram below.
(a) What is the length, in m, of the ladder?
(b) Find the height, in m, of the lamp post.

Solution:


(a)

cos 70 o = 1 h h= 1 cos 70 o h= 1 0.342 h=2.924 m Hence, the length of the ladder =2.924 m

(b)
tan 70 o = T 1 T=tan 70 o ×1    =2.747×1    =2.747 m The height of the lamp post =2.747+1.2 =3.947 m


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