An ecologist wishes to find the height of a redwood tree that is on the other side of a creek, as shown in the figure below. From point A he finds that the angle of elevation to the top of the tree is 12.4°. He then walks 24.8 feet at a right angle from point A to point B. There he finds that the angle between AB and a line extending from B to the tree is 85.1°. What is the height h of the tree?
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Answer:
The height of the redwood tree = 63.60ft
Step-by-step explanation:
From the diagram:
Tan 85.1 = AC/24.8
AC = 24.8 Tan85.1
AC = 289.28 ft
Angle ADC = 90-12.4
Angle ADC= 77.6
Using the Sine Rule
a/SinA = b/SinB = c/SinC
h/Sin12.4 = 289.28/Sin77.7
h = (289.28in12.4)/Sin77.6
h = 63.60 ft
The height of the redwood tree = 63.60ft
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