How do you use theorems about triangles to solve problems?

Step-by-step explanation:

Triangles can be solved if you know either of three pieces of information:

You can solve for the remaining sides and angles using law of sine and law of cosine.

Law of sine:

(sin A) / a = (sin B) / b = (sin C) / c

Law of cosine:

c² = a² + b² − 2ab cos C

Here, A is the angle opposite side a, B is the angle opposite side b, and C is the angle opposite side c.

Law of cosine can also be written as:

b² = a² + c² − 2ac cos B

a² = b² + c² − 2bc cos A

And law of sine can also be written as:

a / (sin A) = b / (sin B) = c / (sin C)

(Notice that when C = 90°, law of cosine becomes Pythagorean theorem.)

15

step-by-step explanation:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)