Answer:
4 √6
Step-by-step explanation:
We have a few right triangles. We know that a²+b²=c², with c being the side opposite the right angle. Representing the side without a value as z, we have:
m²+z² = (8+4)² = 12²
4²+n²=z²
8²+n²=m²
We have 3 equations with 3 unknown variables, so this should be solvable. One way to find a solution is to put everything in terms of m and go from there. First, we can take n out of the equations entirely, removing one variable. We can do this by solving for it in terms of z and plugging that into the third equation, removing a variable as well as an equation.
4²+n²=z²
subtract 4²=16 from both sides
z²-16 = n²
plug that into the third equation
64 + z² - 16 = m²
48 + z² = m²
subtract 48 from both sides to solve for z²
z² = m² - 48
plug that into the first equation
m² + m² - 48 = 144
2m² - 48 = 144
add 48 to both sides to isolate the m² and its coefficient
192 = 2m²
divide both sides by 2 to isolate the m²
96 = m²
square root both sides to solve for m
√96 = m
we know that 96 = 16 * 6, and 16 = 4², so
m = √96 = √(4²*6) = 4 √6
Answer:
cos60°
Step-by-step explanation:
Using the cofunction identity
cos(90 - x) = sinx , then
sin30° = cos(90 - 30)° = cos60°
Answer:
108.43°
Step-by-step explanation:
I graphed this expression on the graph below and found the direction angle of 108.43°.
Find 2 coordinates on the graph : (0, -20) and (10, 10)
Slope = (10 - (-20) ) / (10 - 0) = 30/10 = 3
Slope = 3
y-intercept = (0, - 20)
Equation : y = 3x - 20
Since the right hand side is shaded, the equation is y > 3x - 20.
