Trigonometric Ratios and Applications

The video tutorial explains how to determine the height of a plane using trigonometric ratios, specifically the tangent ratio. It begins by setting up a right triangle problem involving a plane, a person's height, and a horizontal distance. The lesson covers the basics of sine, cosine, and tangent ratios, emphasizing the tangent ratio's application in right triangles. The tutorial demonstrates the use of similar triangles to validate the tangent ratio and applies it to solve the problem of finding the plane's height. The final solution involves calculating the tangent of a given angle and using it to find the unknown height, considering the person's height as well.

What angle is formed between the plane and the person's line of sight?

• 60 degrees

• 90 degrees

• 29 degrees

• 45 degrees

What is the sine of angle A in triangle ABC if the opposite side is 4 and the hypotenuse is 5?

• 0.6

• 0.8

• 0.5

• 0.75

In a right triangle, what does the cosine ratio compare?

• Opposite side to hypotenuse

• Adjacent side to hypotenuse

• Opposite side to adjacent side

• Hypotenuse to opposite side

What is the tangent of a 54-degree angle in triangle AEV if the opposite side is 13.76 and the adjacent side is 10?

• 1.1

• 1.5

• 1.376

• 1.25

Which of the following is true about the tangent ratio?

• It compares the hypotenuse to the opposite side

• It is only applicable in right triangles

• It can be used in all triangles

• It is the same as the sine ratio

What is a common misunderstanding about the tangent ratio?

• It is only for acute angles

• It can be used in all triangles

• It is the same as the sine ratio

• It compares the hypotenuse to the adjacent side

How do you express the tangent of an angle in a right triangle?

• Adjacent side divided by hypotenuse

• Hypotenuse divided by opposite side

• Opposite side divided by adjacent side

• Opposite side divided by hypotenuse

What is the tangent of 29 degrees approximately equal to?

• 0.7

• 0.6

• 0.5543

• 0.5

How high is the plane flying above the ground?

• 300 feet

• 283.26 feet

• 278.26 feet

• 290 feet

What additional height must be added to the calculated height of the plane?

• 6 feet

• 5 feet

• 4 feet

• 3 feet