Trigonometry and Tree Height Calculations

The video tutorial demonstrates how to apply trigonometry to find the height of a tree. The problem involves standing 42 feet away from a tree, with a line of sight 5 feet above the ground, and measuring the angle of elevation to the top of the tree as 43 degrees. By setting up a right triangle and using the tangent function, the length of the side opposite the angle is calculated. The height of the tree is then determined by adding this length to the line of sight height, resulting in a total height of approximately 44.2 feet.

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

• To determine the width of the tree

• To calculate the height of the tree

• To find the distance to the tree

• To measure the angle of elevation

How far is the observer standing from the tree?

• 5 feet

• 43 feet

• 42 feet

• 39.2 feet

What is the angle of elevation to the top of the tree?

• 45 degrees

• 50 degrees

• 43 degrees

• 40 degrees

Which trigonometric function is used to solve for the unknown side?

• Tangent

• Cosine

• Cotangent

• Sine

What is the length of the side opposite the angle of elevation?

• 42 feet

• 5 feet

• 39.2 feet

• 44.2 feet

What is the height of the observer's line of sight from the ground?

• 20 feet

• 15 feet

• 10 feet

• 5 feet

What is the final calculated height of the tree?

• 39.2 feet

• 43 feet

• 42 feet

• 44.2 feet

What is the formula used to calculate the height of the tree?

• Height = X - 5

• Height = X * 5

• Height = X / 5

• Height = X + 5

What is the value of X in the equation used to find the height of the tree?

• 44.2 feet

• 5 feet

• 39.2 feet

• 42 feet

What is the purpose of checking the calculator mode before solving the equation?

• To ensure it is in radian mode

• To ensure it is in degree mode

• To ensure it is in scientific mode

• To ensure it is in standard mode