A plane ascends at a 40-degree angle. When it reaches an altitude of 100 feet, how much ground...


A plane ascends at a {eq}40 ° {/eq} angle. When it reaches an altitude of {eq}100 {/eq} feet, how much ground distance has it covered? To solve, use a trigonometric chart. Round the answer to the nearest tenth.

Tangent of an angle:

We know that for a right angled triangle, tangent of an angle is equal to the perpendicular (opposite) side divided by the adjacent side (base) of the triangle.

Answer and Explanation:

{eq}\tan \theta = \frac{altitude}{base} {/eq}

where base is the ground distance the plane has covered

{eq}0.84=\frac{100}{b} \Rightarrow b=\frac{100}{0.84} = 119.05 \simeq 119 ft {/eq}

Learn more about this topic:

Practice Finding the Trigonometric Ratios

from Geometry: High School

Chapter 14 / Lesson 8

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