How to Solve Trigonometry Problems Using SOHCAHTOA

TL;DR

To solve trigonometry problems using SOHCAHTOA, identify the relevant sides and angles of the triangle. Use the sine, cosine, or tangent ratios to find unknown lengths, such as side lengths or heights, based on given measures. This method is essential for solving problems involving right triangles.

Transcript

We're on problem 66. In the accompanying diagram, the measure of angle a is 32 degrees. And AC is equal to 10. Which equation could be used to find x in triangle ABC? So we want x. So let's write our SOHCAHTOA down. What are they giving us? Well x is the opposite side, this is equal to the opposite, it's opposite of our angle in question. And then ... Read More

Key Insights

• 🥳 Trigonometry problems often involve using the ratios from SOHCAHTOA to find side lengths or heights in right triangles.
• 🥳 30-60-90 triangles have specific ratios between side lengths, making them useful for quick calculations.
• 🌲 Trigonometry can be applied to real-world scenarios, such as finding the height of a tree or the distance up a wall reached by a ladder.

Questions & Answers

Q: How is SOHCAHTOA used to find side lengths in a triangle?

SOHCAHTOA is used to identify which trigonometric function can be applied in a given scenario. Based on the given information, the appropriate function is chosen to find the desired side length using ratios.

Q: Why are 30-60-90 triangles useful?

30-60-90 triangles have specific ratios between their side lengths, which make them easy to work with. Memorizing these ratios allows for quick calculations in problems involving these types of triangles.

Q: Can trigonometry be used to find heights of objects?

Yes, trigonometry can be used to find heights of objects by measuring the angle of elevation and the distance between the observer and the object. By using the appropriate trigonometric function, such as sine or tangent, the height can be calculated.

Q: How can 30-60-90 triangles be identified?

In a 30-60-90 triangle, the angles measure 30 degrees, 60 degrees, and 90 degrees. The side lengths have specific ratios: the hypotenuse is twice the length of the shorter leg, and the longer leg is √3 times the length of the shorter leg.

Summary & Key Takeaways

• Problem 66: The tangent of 32 degrees is used to find side length x in triangle ABC, resulting in x = 10 tangent 32 degrees.

• Problem 67: The cosine of 53 degrees is used to find the distance up the wall the ladder reaches, resulting in x = 8 cosine 53 degrees, approximately 4.8.

• Problem 68: The sine of 24 degrees is used to find the length of JK, resulting in JK = 28 sine 24 degrees.

• Problem 69: The sine of 50 degrees is used to find the approximate height of the tree, resulting in the height of the tree = 100 sine 50 degrees, approximately 76.6.

• Problem 70: The side length a is given as 3 root 3. By using 30-60-90 triangle properties, the side length b is found to be 9.