Solving Right Triangles: Finding the Missing Side of Triangle (SOH - CAH - TOA)

Summary

In this video, the teacher explains how to solve for missing sides of right triangles using the SOHCAHTOA method. The video covers two examples where the sine, cosine, and tangent ratios are applied to calculate unknown sides based on given angles and side lengths. The first example uses sine to find the opposite side, and the second uses tangent to determine the opposite side. The video includes step-by-step instructions and encourages viewers to practice with a problem at the end. Viewers are also encouraged to like, subscribe, and comment their answers.

Takeaways

• 😀 Understand the basic trigonometric ratios: SOH (Sine = Opposite / Hypotenuse), CAH (Cosine = Adjacent / Hypotenuse), and TOA (Tangent = Opposite / Adjacent).
• 😀 Use the **SOH-CAH-TOA** method to solve for missing sides in right triangles.
• 😀 In the first example, use the **SOH** ratio to solve for the opposite side when given the angle and hypotenuse.
• 😀 Cross-multiply to solve the equation when using trigonometric ratios to find missing sides in a right triangle.
• 😀 For the first example, the missing side X is calculated as 5.9 cm after applying **sin(36°) = X / 10**.
• 😀 In the second example, use the **TOA** ratio (Tangent = Opposite / Adjacent) to solve for the opposite side when given the adjacent side and angle.
• 😀 The **TOA** method for the second example leads to a final result of X = 5 cm after solving **tan(40°) = X / 6**.
• 😀 Encourage the use of scientific calculators to simplify trigonometric calculations (e.g., sin(36°), tan(40°)).
• 😀 Make sure to round the final answers to one decimal place for clarity and consistency.
• 😀 Engage the audience with interactive practice problems, asking them to solve a new triangle problem in the comments section.
• 😀 End the video with a call to action for viewers to like, subscribe, and stay updated on future educational content.

Q & A

What is the purpose of using SOH-CAH-TOA in solving right triangles?

SOH-CAH-TOA is used to remember the three main trigonometric ratios (sine, cosine, and tangent) that help solve for missing sides in right triangles. Each part corresponds to a different relationship between the sides of a right triangle based on the given angle.

What does SOH stand for and what does it represent?

SOH stands for 'Sine = Opposite / Hypotenuse.' This means that the sine of an angle in a right triangle is the ratio of the length of the opposite side to the hypotenuse.

In the first example, why is the hypotenuse used with the sine function?

In the first example, the sine function is used because we are given the hypotenuse (10 cm) and the missing side is the opposite side to the given acute angle (36°). The sine ratio involves the opposite side and the hypotenuse.

What steps are involved in solving for the missing side using the sine function?

First, identify the correct trigonometric ratio based on the given sides (in this case, sine for opposite and hypotenuse). Then, write the equation (sin(angle) = opposite / hypotenuse). After substituting the known values, solve for the missing side using basic algebra, such as multiplying both sides of the equation.

In the second example, why is the tangent function used instead of sine or cosine?

In the second example, the tangent function is used because the known side is the adjacent side (6 cm) and the missing side is the opposite side. The tangent ratio (TOA) relates the opposite side to the adjacent side.

How do you solve for the missing side using the tangent function?

First, identify the correct trigonometric ratio, which is tangent (opposite / adjacent). Then, set up the equation (tan(angle) = opposite / adjacent). After substituting the known values, solve for the missing side by multiplying both sides of the equation by the adjacent side.

Why is rounding important when solving for missing sides in trigonometry?

Rounding is important because trigonometric calculations often result in long decimal numbers. For clarity and practical use, these numbers are rounded to a certain decimal place, such as one decimal point or two, depending on the instructions or context.

What is the significance of using a scientific calculator in these problems?

A scientific calculator is essential for accurately calculating trigonometric functions like sine, cosine, and tangent. It ensures precision when determining the values of these functions, which is crucial for solving for the missing sides.

What is the final result for the missing side in the first example?

The final result for the missing side in the first example is approximately 5.9 cm, which is the length of the opposite side based on the sine function.

In the second example, why is the final answer for the missing side 5 cm instead of 5.0 cm?

The final answer is 5 cm because, after using the tangent function and calculating, the result is 5.0 cm, which rounds to 5 cm when expressed as a whole number.