Solving using trig and trig word problems

Front

What is the definition of the sine function in a right triangle?

Back

The sine function is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the definition of the cosine function in a right triangle?

Back

The cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the definition of the tangent function in a right triangle?

Back

The tangent function is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Front

How do you find the length of a shadow using the angle of elevation?

Back

Use the formula: Shadow length = height / tan(angle of elevation).

Front

If Jake is 6 ft tall and the angle of elevation of the sun is 28 degrees, how long is his shadow?

Back

Shadow length = 6 / tan(28°) ≈ 11.3 feet.

Front

What is the relationship between the sides of a right triangle and the sine function?

Back

For angle θ, sin(θ) = opposite/hypotenuse.

Front

What is the relationship between the sides of a right triangle and the cosine function?

Back

For angle θ, cos(θ) = adjacent/hypotenuse.

Front

What is the relationship between the sides of a right triangle and the tangent function?

Back

For angle θ, tan(θ) = opposite/adjacent.

Front

How do you solve for an unknown side using sine?

Back

Rearrange the sine ratio: sin(θ) = opposite/hypotenuse to find opposite = hypotenuse * sin(θ).

Front

How do you solve for an unknown side using cosine?

Back

Rearrange the cosine ratio: cos(θ) = adjacent/hypotenuse to find adjacent = hypotenuse * cos(θ).