Trigonometric Ratios and Applications

Kevin visits New York City and wonders about the height of the Statue of Liberty. By observing the angle from the base to the torch, he uses trigonometric ratios to form a right triangle. The video explains sine, cosine, and tangent ratios, focusing on using the tangent ratio to calculate the statue's height. The process involves setting up an equation and using a calculator to find the tangent of the angle, then multiplying by the distance to the platform. The video concludes with a reflection on the practicality of trigonometry.

What angle did Kevin observe between the base and the torch of the Statue of Liberty?

• 8°

• 12.5°

• 15°

• 10.5°

Which trigonometric ratios are introduced to calculate unknown heights?

• Sine, Secant, Cosecant

• Sine, Cosine, Tangent

• Tangent, Cotangent, Secant

• Cosine, Cotangent, Secant

What is the purpose of using trigonometric ratios in this context?

• To calculate unknown heights

• To measure angles

• To find distances

• To determine area

What shape is formed when using the angle and distance to calculate the height?

• Right Triangle

• Equilateral Triangle

• Isosceles Triangle

• Scalene Triangle

What is the significance of the right angle in forming the triangle?

• It calculates the area

• It measures the height

• It determines the base

• It helps identify the hypotenuse

What is the side opposite the right angle in a right triangle called?

• Base

• Opposite Leg

• Adjacent Leg

• Hypotenuse

What is the adjacent leg in a right triangle?

• The longest side

• The side opposite the angle

• The base of the triangle

• The side between the angle and the right angle

How do you calculate the sine of an angle in a right triangle?

• Adjacent leg divided by hypotenuse

• Opposite leg divided by hypotenuse

• Opposite leg divided by adjacent leg

• Hypotenuse divided by opposite leg

What is the tangent of an angle in a right triangle?

• Opposite leg divided by adjacent leg

• Adjacent leg divided by hypotenuse

• Hypotenuse divided by opposite leg

• Opposite leg divided by hypotenuse

What is the cosine of an angle in a right triangle?

• Hypotenuse divided by opposite leg

• Adjacent leg divided by hypotenuse

• Opposite leg divided by hypotenuse

• Opposite leg divided by adjacent leg