Trigonometry - How To Solve Right Triangles

TL;DR

Determine the value of h in a larger right triangle with two triangles inside, given angles and side lengths.

Transcript

in this video we're going to talk about how to solve right triangles but we have a special case we have two triangles in a larger triangle and our goal is to calculate the value of h so we know that this portion is 500 and given the two angles 30 and 60 degrees what is the value of h of this larger right triangle feel free to pause the video and tr... Read More

Key Insights

• 🔺 The problem involves solving a right triangle with two smaller triangles inside, leading to a system of equations.
• 🥳 The tangent ratio is used to write equations involving h in both the smaller and larger right triangles.
• ⛱️ By solving the system of equations, the value of h is determined to be approximately 433.01 or rounded to the nearest whole number as 433.
• 😀 The exact expression for h is 250√3.
• 🙃 Labeling the sides and using trigonometric ratios is a useful approach in solving right triangles.
• 🔺 Understanding the 30-60-90 triangle can be helpful in determining values for trigonometric functions.
• 👨‍💼 The principles of SOHCAHTOA (sine, cosine, tangent) are utilized in solving the problem.

Questions & Answers

Q: What is the goal of the problem described in the video?

The goal is to calculate the value of h in a larger right triangle with two triangles inside, given specific angles and side lengths.

Q: What is the first step in solving this problem?

The first step is to label the sides of the smaller right triangle and use the tangent ratio to write an equation involving h.

Q: How is the value of h found using the tangent ratio?

By substituting the known values into the equation tan(60°) = h/x, the equation can be rearranged and solved for h.

Q: Why is a second equation necessary to solve for h?

In order to solve for two variables, x and h, a second equation is needed. This equation is obtained by using the tangent ratio in the larger right triangle.

Q: How is the system of equations solved to find the value of h?

By simplifying and manipulating the equations, the system can be solved by isolating the variable h. After solving the equations, the value of x is found to be 250.

Q: How is the final value of h calculated?

The value of x is substituted into one of the original equations to find the value of h, which is approximately 433.01.

Q: Can the final answer for h be rounded to the nearest whole number?

Yes, the final answer can be rounded to the nearest whole number, resulting in h ≈ 433.

Q: What is the exact expression for h?

The exact expression for h is 250√3.

Summary & Key Takeaways

• The problem involves calculating the value of h in a larger right triangle with two smaller triangles inside.

• The first step is to label the sides of the smaller right triangle and use the tangent ratio to write an equation involving h.

• Another equation is needed, which is obtained by focusing on the larger right triangle and using the tangent ratio again.

• By solving the system of equations, the value of h is found to be approximately 433.01.