Applying Trigonometric Functions

In summary, the conversation revolved around applying basic trigonometric functions to solve right triangles and the difficulty in manipulating them for more complex questions involving non-right triangles. The objective was to find the length of line segment TU using only basic trigonometric functions, with no use of sine or cosine laws. The solution involved assigning variables to the given line segments and creating two equations in two unknowns using the tangent function.
  • #1
soccerstar814
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Okay, so I know how to apply basic trigonometric functions to solve right triangles. However, I am not quite sure how to manipulate trigonometric functions to solve for more complex questions involving non-right triangles, like the question I have attached. I have to use the basic trigonometric functions only to solve this question (no sine law or cosine law, etc.) My objective is to find the length of line segment TU. Any help would be greatly appreciated! Thanks.
 

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  • #2
I would let $x=\overline{UV}$ and $y=\overline{TU}$ then state:

\(\displaystyle \tan(53.8^{\circ})=\frac{y}{x}\)

\(\displaystyle \tan(38.8^{\circ})=\frac{y}{x+12.5}\)

Now you have two equations in two unknowns...
 

FAQ: Applying Trigonometric Functions

What are the common applications of trigonometric functions?

Trigonometric functions are used to model and measure various real-world phenomena, such as the motion of objects, sound waves, and electrical currents. They are also used in fields like engineering, architecture, and astronomy to calculate angles, distances, and heights.

How do I apply trigonometric functions to solve real-life problems?

To apply trigonometric functions, you first need to identify the relevant angles and sides in the problem and assign them to the appropriate trigonometric ratio (sine, cosine, or tangent). Then, use the trigonometric formula or calculator to find the missing values.

What is the difference between sine, cosine, and tangent?

Sine (sin) is the ratio of the opposite side to the hypotenuse, cosine (cos) is the ratio of the adjacent side to the hypotenuse, and tangent (tan) is the ratio of the opposite side to the adjacent side in a right triangle. These ratios are used to calculate angles and distances in trigonometry.

Can you give an example of a real-life problem that can be solved using trigonometric functions?

One example is determining the height of a building using trigonometric functions. By measuring the angle of elevation from a known distance, and using the tangent function, you can calculate the height of the building without needing to physically measure it.

How does understanding trigonometric functions benefit me in my daily life?

Understanding trigonometric functions can be beneficial in various ways, such as helping you navigate using maps, understanding sound and light waves, and even playing sports like golf or baseball. It also improves problem-solving skills and critical thinking abilities.

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