Trigonometric Ratios and Applications

The video tutorial explains how to find the length of a ladder needed to reach a roof using trigonometry. It introduces the cosine ratio, which relates the length of the side adjacent to an acute angle to the hypotenuse in right triangles. The tutorial reviews the sine ratio and demonstrates the application of the cosine ratio in similar triangles. Finally, it applies the cosine ratio to solve the problem of determining the ladder's length, emphasizing the importance of using a scientific calculator for accurate results.

What is the height of the house in the ladder problem?

• 20 feet

• 15 feet

• 12 feet

• 10 feet

Which angle is used to position the ladder in the problem?

• 35 degrees

• 50 degrees

• 30 degrees

• 45 degrees

What is the sine of an angle defined as?

• Hypotenuse divided by opposite side

• Opposite side divided by hypotenuse

• Adjacent side divided by hypotenuse

• Opposite side divided by adjacent side

In triangle ABC, what is the length of the hypotenuse if the opposite side is 3.5 inches and the angle is 38 degrees?

• 5.7 inches

• 4.5 inches

• 6.0 inches

• 5.0 inches

What is the cosine ratio in a right triangle?

• Opposite side divided by hypotenuse

• Adjacent side divided by hypotenuse

• Opposite side divided by adjacent side

• Hypotenuse divided by adjacent side

In triangle ADG, what is the cosine of the 35-degree angle?

• 0.819

• 0.614

• 0.714

• 0.919

Why can't the cosine ratio be used in all triangles?

• It only applies to isosceles triangles

• It only applies to right triangles

• It only applies to equilateral triangles

• It only applies to scalene triangles

What is the approximate length of the ladder needed to reach the roof?

• 15.5 feet

• 14.65 feet

• 13.5 feet

• 12.5 feet

What is the cosine of 35 degrees approximately equal to?

• 0.819

• 0.619

• 0.719

• 0.919

What should the man consider when choosing a ladder length?

• It should be slightly longer than 14.65 feet

• It should be exactly 14.65 feet

• It should be exactly 12 feet

• It should be shorter than 14.65 feet