CA Geometry: Basic trigonometry | Worked examples | Geometry | Khan Academy

TL;DR

This video explains how to solve various trigonometry problems involving angles, triangles, and equations.

Transcript

We're on problem 61. It says the point minus 3, 2 lies on a circle whose equation is x plus 3 squared plus y plus 1 squared is equal to r squared. Which of the following must be the radius of the circle? So the way to think about it is, is that this point satisfies this equation. Any point on the equation will satisfy both sides of this equality si... Read More

Key Insights

• 🙃 Trigonometry problems often involve using ratios of sides in right triangles.
• 🥳 The SOHCAHTOA mnemonic is a helpful tool to remember trigonometric ratios.
• 🆘 Substituting coordinates into equations can help find missing values in geometric problems.
• 🗯️ The Pythagorean theorem is useful for finding unknown side lengths in right triangles.

Questions & Answers

Q: How do you solve Problem 61 using the given equation?

To solve Problem 61, substitute the x and y values of the given point into the equation and solve for r. In this case, the radius, r, turns out to be 3.

Q: What does the mnemonic SOHCAHTOA stand for and how is it used?

SOHCAHTOA stands for sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent. It helps to remember the ratios of the trigonometric functions for different angles in a right triangle.

Q: How do you solve Problem 62 using trigonometric ratios?

In Problem 62, you are given sin(x) = 5/13. Using the SOHCAHTOA mnemonic, you can find that cos(x) = 12/13 and tan(x) = 5/12.

Q: How do you find the length of AC in Problem 63?

In Problem 63, you are given sin(A) = 0.7. Use the SOHCAHTOA mnemonic to set up the equation sin(A) = opposite/hypotenuse and solve for the length of AC, which is equal to 30.

Q: How do you determine the height of a street light in Problem 64?

In Problem 64, you are given the tangent of an angle and the length of the adjacent side. Use the tangent ratio (opposite/adjacent) to set up an equation and solve for the unknown height.

Q: Why is choice C the correct answer in Problem 65?

In Problem 65, you need to use the proper trigonometric ratio for the given angle to find the value of BC. The tangent of 58 degrees (opposite/adjacent) is equal to 8.2/BC, making choice C the correct answer.

Summary & Key Takeaways

• Problem 61: The point (2, -3) lies on a circle with equation (x+3)^2 + (y+1)^2 = r^2. We can substitute the coordinates of the point into the equation to find that the radius, r, must be equal to 3.

• Problem 62: Given that sin(x) = 5/13, we can use the SOHCAHTOA mnemonic to find that cos(x) = 12/13 and tan(x) = 5/12.

• Problems 63-65: These problems involve using trigonometric ratios to find missing side lengths or angles in right triangles.