DSAT DSAT Geometry and Trigonometry 2

Question 1

In a 30-60-90 triangle, the side opposite the 30° angle is 6. What is the length of the hypotenuse?

Accepted Answer

12

Answer

In a 30-60-90 triangle, the hypotenuse is twice the shortest side: 2 × 6 = 12.

Question 2

What is the slope of a line passing through the points (2, 3) and (6, 11)?

Accepted Answer

2

Answer

Slope = (y₂ − y₁) / (x₂ − x₁) = (11 − 3) / (6 − 2) = 8 / 4 = 2.

Question 3

A sector of a circle has a central angle of 90° and a radius of 8. What is the area of the sector?

Accepted Answer

16π

Answer

Area of a sector = (θ/360) × πr² = (90/360) × π(64) = (1/4) × 64π = 16π.

Question 4

The exterior angle of a triangle measures 120°. If one of the non-adjacent interior angles is 45°, what is the other non-adjacent interior angle?

Accepted Answer

75°

Answer

An exterior angle equals the sum of the two non-adjacent interior angles: 120° = 45° + x, so x = 75°.

Question 5

If sin(θ) = 3/5 in a right triangle, what is cos(θ)?

Accepted Answer

4/5

Answer

Using a 3-4-5 right triangle where sin(θ) = 3/5, the adjacent side is 4, so cos(θ) = 4/5.

(DSAT) Digital SAT Practice Test