Math--Applications in Trigonom

小芝芝

2011-05-19 2:35 am

please to sove the collowing questions:

1. The figure shows a part of a contour map of scale 1:100 000. The lengths
of the straight roads AB and CB on the map are 2.2cm and 3.1cm
respectively. Which road is steeper? Explain your answer briefly.

2. Two buildings A and B are 35m apart. The angle of elevation of the top
of building B from the foot of building A is 58度. If building A is 70m
tall, find the angle of depression of the top of building B from the top
of building A.

回答 (1)

Godfrey

2011-05-19 7:13 pm

✔ 最佳答案

Figure is missing in question 1.

Question 2

A F
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E B
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C---------D

CD is the ground level. CD = 35 m, AC = 70 m and angle BCD = 58 度
Find angle of depression FAB
Let the top of building A be A and top of building B be B.
tan 58度 = BD/CD
1.6003 = BD/35 m
BD = 35 m x 1.6003 = 56.0117 m (Building B is 56.0117 m tall)
FB = Height of building A – Height of building B = 70 m – 56.01 17 m = 13.9883 m
AF = CD = 35 m
tan angle FAB = FB/AF
tan angle FAB = 13.9883 m/35 m = 0.3997
angle FAB = tan^1(0.3997) = 21.78 度

angle of depression of the top of building B from the top of building A = 21.78 度.

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