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How can understanding trigonometry help in real-life situations?

Trigonometry can be a powerful tool in solving various real-life problems. Let's take a look at an example:

The pilot of an airplane wants to fly due north, but there is a 65 km/h wind blowing from east to west. In what direction should the pilot head her plane if its speed relative to the air is 340 km/h?

Answer:

The pilot should head her plane 10.8° north of east.

Trigonometry helps us solve problems involving angles and sides of triangles. In this scenario, the pilot needs to calculate the direction to head her plane considering the wind speed and the speed of the plane.

By applying the tangent function (tan), we can determine the angle the pilot should navigate the plane. The calculation involves finding the ratio of the opposite side (wind speed) to the adjacent side (plane speed) of the triangle formed by the wind and the plane's motion.

Using the formula tan(θ) = opposite/adjacent, we can substitute in the given values to find the angle θ. After performing the calculations, the result is 10.8° north of east. This means the pilot should steer the plane slightly towards the northeast direction to counteract the effect of the crosswind blowing from east to west.

This example illustrates how trigonometry can be applied to real-life situations, allowing individuals to make informed decisions by understanding angles and relationships between various elements. By mastering mathematical concepts like trigonometry, we can navigate challenges and reach new heights with precision and accuracy.