Anyone have answers for Connexus Geom G B 2532 Unit 3 Right Triangles and Trigonometry Unit Test?
The Correct Answer and Explanation is:
Trigonometry in right triangles generally involves understanding the relationships between the angles and sides of the triangle using the following primary trigonometric functions:
- Sine (sin): The ratio of the opposite side to the hypotenuse.
- sin(θ)=oppositehypotenuse\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}sin(θ)=hypotenuseopposite
- Cosine (cos): The ratio of the adjacent side to the hypotenuse.
- cos(θ)=adjacenthypotenuse\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}cos(θ)=hypotenuseadjacent
- Tangent (tan): The ratio of the opposite side to the adjacent side.
- tan(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}tan(θ)=adjacentopposite
These functions allow you to solve for unknown sides or angles in a right triangle if you know some of the sides or angles.
To solve problems, you may need to:
- Use the Pythagorean Theorem for finding missing side lengths in right triangles:
- a2+b2=c2a^2 + b^2 = c^2a2+b2=c2 (where aaa and bbb are the legs, and ccc is the hypotenuse).
- Apply trigonometric identities such as:
- sin2(θ)+cos2(θ)=1\sin^2(\theta) + \cos^2(\theta) = 1sin2(θ)+cos2(θ)=1
