AST Geometry and Trigonometry 3

Question 1

In a right triangle, sin(θ) is defined as which ratio?

Accepted Answer

opposite/hypotenuse

Answer

By SOHCAHTOA, sine equals the ratio of the opposite side to the hypotenuse.

Question 2

What is the value of cos(60°)?

Accepted Answer

1/2

Answer

cos(60°) = 1/2 is a standard unit circle value.

Question 3

What does the Pythagorean trigonometric identity state?

Accepted Answer

sin²(θ) + cos²(θ) = 1

Answer

The fundamental Pythagorean identity is sin²(θ) + cos²(θ) = 1 for all angles θ.

Question 4

If tan(θ) = 1 and 0° < θ < 90°, what is θ?

Accepted Answer

45°

Answer

tan(45°) = 1 because sin(45°) = cos(45°) = √2/2, making their ratio equal to 1.

Question 5

A 10-foot ladder leans against a wall making a 60° angle with the ground. How high up the wall does it reach?

Accepted Answer

5√3 feet

Answer

sin(60°) = height/10, so height = 10 × (√3/2) = 5√3 feet.

AST - ACT Scaling Test Practice Test