Tangent and Angle of Elevation

This video tutorial explains how to solve an angle of elevation problem using trigonometry. The problem involves finding the height of a tree when the angle of elevation changes from 45 degrees to 60 degrees as the observer moves 50 meters closer to the tree. The tutorial sets up trigonometric equations using tangent functions for both angles, solves these equations to express the height and distance in terms of each other, and finally calculates the tree's height by substituting and simplifying the expressions.

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

• To find the distance between two trees

• To determine the speed of a moving car

• To calculate the height of a tree

• To measure the angle of a building

What happens to the angle of elevation as the observer moves 50 meters closer to the tree?

• It decreases from 60 degrees to 45 degrees

• It decreases from 45 degrees to 30 degrees

• It increases from 45 degrees to 60 degrees

• It remains constant at 45 degrees

What is the initial distance between the observer and the tree?

• 50 meters

• 100 meters

• 150 meters

• 200 meters

What is the significance of the angle of elevation in this problem?

• It measures the width of the tree

• It determines the speed of the observer

• It is used to find the height of the tree

• It helps in calculating the distance

What is the role of the observer in this problem?

• To measure the width of the tree

• To calculate the speed of the tree

• To observe the change in angle of elevation

• To determine the color of the tree

Which trigonometric function is used to solve the problem?

• Sine

• Cosine

• Tangent

• Cotangent

How is the tangent of an angle defined?

• Opposite side divided by adjacent side

• Adjacent side divided by opposite side

• Hypotenuse divided by opposite side

• Adjacent side divided by hypotenuse

What mathematical concept is primarily used in this problem?

• Calculus

• Trigonometry

• Geometry

• Algebra

What is the value of tangent 60 degrees?

• 1/2

• Square root of 3

• 2

• 1

What equation is derived from tangent 60 degrees?

• X = H + square root of 3

• X = H / square root of 3

• X = H - square root of 3

• X = H * square root of 3