Applications and Solving Right Triangles • Section 1.3 15 Example 1.13 A blimp 4280 ft above the ground measures an angle of depression of 24 ◦ from its horizontal line of sight to the base of a house on the ground. Assuming the ground is Fat, how far away along the ground is the house from the blimp? 24 ◦ 4280 θ x Solution: Let x be the distance along the ground from the blimp to the house, as in the picture to the right. Since the ground and the blimp’s horizontal line of sight are parallel, we know from elementary geometry that the angle of elevation θ from the base of the house to the blimp is equal to the angle of depression from the blimp to the base of the house, i.e. θ = 24 ◦ . Hence, 4280 x = tan 24 ◦ ⇒ x = 4280 tan 24 ◦ = 9613 ft . Example 1.14 An observer at the top of a mountain 3 miles above sea level measures an angle of depression of 2.23 ◦ to the ocean horizon. Use this to estimate the radius of the earth. r
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