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# mathematics (Trigonometry)

1. Two lighhouses A &amp; B are on a straight coastline extending from north to south. The bearings of ship C from A is S42E and from B is N67E. If the shortest distance of the ship from the shore is 5 km, find the distance betwwn the two lighthouses. (ans: 7.68)

2.From a building 25 m above the ground level, the angles of depression of the top and the bootom of a lamp-post are 26 (degree) and 33 (degree) respectively. What is the height of the lamp-post? (ans.6.22)

3.A ballon is located at point A at noon.At that time, the ballon is fixed at a position 50 m above the ground by a rope tied at pointed P. The angle of elevation from point P to point A is 20(degree). Suddenly, the wind causes the ballon to fly up to point B.X &amp; Y are vertical projections of A&amp;B respectively with XY=18m.

(a) find the length of the rope. ans.146m

(b) find the distance bewteen P and Y. ans. 119m

(c) find the height of B above the ground ans 84.4m

Write the step by step. Please Quick

### 1 個解答

• 最愛解答

(1) Let the point on the shore closest to C be X.

CX = 5km

tan 42 = CX/AX => AX = CX/tan 42

tan 67 = CX/BX => BX = CX/tan 67

AB = AX + BX = CX/tan42 + CX/tan67

= 5/0.9 + 5/2.356 = 5.553 + 2.122 = 7.68km

(2) Let the horizontal distance between the building and lamp post be x m

25/x = tan33

x = 25/tan33 = 38.50 m

Vertical distance between building and top of lamp post

= 38.50 tan26

= 18.78

Height of lamp post = 25 - 18.78 = 6.22m

3. (a) 50 / (length of rope) = sin20

Length of rope = 50/sin20 = 146 m

(b) The distance between P and X = 146 * cos20 = 137 m

The distance between P and Y = 137 - 18 = 119 m

(c) Let the angle of elevation for B be u

cos u = 119/146 = 0.8166

u = 35.26 degrees

Height of B = 146 * sin 35.26 = 84.4 m