Solving for h in Triangles

This video tutorial explains how to solve a right triangle problem involving two smaller triangles within a larger triangle. The goal is to find the value of h using given angles and side lengths. The instructor uses trigonometric ratios, specifically tangent, to set up equations for both the small and large triangles. By equating these expressions, the instructor solves for the unknown variables, x and h, providing both exact and approximate solutions. The tutorial emphasizes the importance of labeling and systematically solving geometric problems.

What is the main objective of the problem discussed in the video?

• To measure the angles of the triangle

• To determine the value of h

• To calculate the area of the triangle

• To find the value of x

Which trigonometric ratio is used to find the first equation involving h?

• Sine

• Cosine

• Tangent

• Secant

What is the value of tangent of 60 degrees used in the first equation?

• 2

• 1/2

• Root 3

• 1

Why is a second equation necessary to solve for h?

• To calculate the area

• To find the hypotenuse

• To solve for two variables

• To verify the first equation

What is the tangent of 30 degrees used in the second equation?

• 2

• 1

• Root 3

• 1/Root 3

What operation is performed to eliminate the fractions in the second equation?

• Addition

• Multiplication

• Subtraction

• Division

What is the value of x found after solving the equations?

• 200

• 250

• 150

• 300

How is the value of h expressed in its exact form?

• 250

• 250 times the square root of 3

• 500

• 433.01

What is the approximate decimal value of h?

• 433.01

• 300

• 500

• 250

What is the final step to find the value of h after determining x?

• Use the second equation

• Use the first equation

• Recalculate the angles

• Find the hypotenuse