Trigonometric Ratios in Application Problems

The video by Amal Kumar explains when to use different trigonometric ratios to solve application problems. It covers the primary trigonometric ratios: sine, cosine, and tangent, and introduces the mnemonic 'sohcahtoa' to remember them. The video provides examples, such as calculating the height of a kite using sine and cosine, and determining the angle and length of a ladder using tangent and sine. The video concludes by emphasizing the use of multiple trigonometric ratios in solving real-world problems.

What is the primary purpose of trigonometric ratios?

• To measure distances directly

• To solve application problems involving right triangles

• To calculate angles in any triangle

• To solve algebraic equations

Which mnemonic helps in remembering trigonometric ratios?

• PEMDAS

• SOHCAHTOA

• FOIL

• BODMAS

In the kite example, which trigonometric ratio is used to find the height?

• Secant

• Sine

• Tangent

• Cosine

What is the angle of elevation in the kite example?

• 30 degrees

• 45 degrees

• 50 degrees

• 60 degrees

How is the height of the kite calculated using the sine ratio?

• 1000 * tan(50 degrees)

• 1000 * sin(50 degrees)

• 1000 * cos(50 degrees)

• 1000 / sin(50 degrees)

Which trigonometric ratio is used to find the horizontal distance in the kite example?

• Cosine

• Sine

• Cosecant

• Tangent

What is the horizontal distance from the kite to the point on the ground?

• 1000 meters

• 766 meters

• 642.78 meters

• 500 meters

In the ladder example, which trigonometric ratio is used to find the angle of inclination?

• Cotangent

• Tangent

• Cosine

• Sine

What is the angle of inclination of the ladder with the horizontal?

• 78.7 degrees

• 60 degrees

• 90 degrees

• 45 degrees

How is the length of the ladder calculated using the sine ratio?

• 10 / cos(78.7 degrees)

• 10 * sin(78.7 degrees)

• 10 / sin(78.7 degrees)

• 10 * cos(78.7 degrees)