Question

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?

Answer 1

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