Trigonometric Functions and Right Triangles

The video tutorial explains how to find the missing side of a right triangle using trigonometry. It begins by identifying the known values, such as the hypotenuse, and the side to be found. The tutorial then guides the viewer in choosing the correct trigonometric function, cosine, based on the known sides. It proceeds to set up the equation and solve it using algebra, ensuring the calculation is done in degree mode for accuracy. The final answer is calculated to the nearest tenth.

What is the primary goal when using trigonometry to find a missing side in a right triangle?

• To find the measure of an angle

• To find the area of the triangle

• To determine the length of a missing side

• To calculate the perimeter of the triangle

Which side of a right triangle is known as the hypotenuse?

• The side adjacent to the right angle

• The shortest side of the triangle

• The longest side of the triangle

• The side opposite the right angle

What is the length of the hypotenuse in this problem?

• 10 units

• 20 units

• 18 units

• 15 units

Which angle is adjacent to the side we are trying to find?

• 30°

• 50°

• 40°

• 60°

Which trigonometric function is used when you know the adjacent side and the hypotenuse?

• Cosine

• Sine

• Secant

• Tangent

Which trigonometric function would you use if you knew the opposite side and the hypotenuse?

• Cotangent

• Tangent

• Cosine

• Sine

If the angle was 50° instead of 40°, which trigonometric function would still be appropriate given the same known sides?

• Sine

• Cosine

• Secant

• Tangent

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

• Opposite side over hypotenuse

• Adjacent side over hypotenuse

• Hypotenuse over adjacent side

• Opposite side over adjacent side

How do you set up the equation to find the missing side using cosine?

• cos(40°) = X / 18

• sin(40°) = X / 18

• cos(40°) = 18 / X

• tan(40°) = X / 18

What is the general formula for cosine in a right triangle?

• cos(θ) = hypotenuse / opposite

• cos(θ) = adjacent / hypotenuse

• cos(θ) = opposite / hypotenuse

• cos(θ) = hypotenuse / adjacent