Trigonometry and Law of Cosines

The video tutorial explains how to model a steep mountain as a right triangle with a 72-degree inclination and a height of 3500 feet. It describes setting up a cable car path from a point 800 feet from the mountain's base to its peak. The tutorial uses trigonometry to find side lengths and applies the law of cosines to calculate the shortest cable length needed, approximately 4000.35 feet.

What is the angle of inclination of the mountain to the horizontal?

• 90 degrees

• 60 degrees

• 72 degrees

• 45 degrees

How far is the starting point of the cable car from the base of the mountain?

• 1200 feet

• 800 feet

• 1000 feet

• 500 feet

Which trigonometric function is used to find the length of side AB?

• Secant

• Tangent

• Sine

• Cosine

What is the approximate length of side AB calculated using the sine function?

• 4500 feet

• 4000 feet

• 3680.12 feet

• 3500 feet

Which law is applied to find the length of the cable car path?

• Law of Sines

• Law of Cosines

• Pythagorean Theorem

• Law of Tangents

What is the measure of angle BAD in the obtuse triangle?

• 180 degrees

• 72 degrees

• 108 degrees

• 90 degrees

What is the formula used to calculate the length of side BD using the law of cosines?

• c^2 = a^2 + b^2 - 2ab cos(C)

• c^2 = a^2 - b^2 + 2ab cos(C)

• c^2 = a^2 + b^2 + 2ab cos(C)

• c^2 = a^2 - b^2 - 2ab cos(C)

What is the calculated value of c squared in the final step?

• 16,283,834.61

• 15,000,000.00

• 18,000,000.00

• 20,000,000.00

What is the approximate shortest length of the cable needed?

• 4500 feet

• 4000.35 feet

• 3680 feet

• 3500 feet

Why is the principal square root taken in the final calculation?

• To determine the hypotenuse

• To calculate the angle

• To ensure the length is positive

• To find the area of the triangle