Complete the paragraph proof You can use the similar triangles formed by the altitude to write ratios for corresponding sides. Using ratios from the large and medium triangles, & = valf vl. This can be rewritten as ✓ cf=a? Using ratios from the large and small triangles, c/bv This can be rewritten as 62 = ec. By substitution, a2 + b2 = cf + ec v You can then factor as a + b2 = clf + e). From the large triangle, you know (f+e) =VC So, a2 + b2 = c2 by using substitution. (awnsers are up above)​

Based on the diagram, match the trigonometric ratios with the corresponding ratios of the sides of the triangle. tiles : cosb sinb tanb sincposs matches: c/b b/a b/c c/a

In new york city at the spring equinox there are 12 hours 8 minutes of daylight. the longest and shortest days of the year very by two hours and 53 minutes from the equinox in this year the equinox falls on march 21 in this task you use trigonometric function to model the hours of daylight hours on certain days of the year in new york city a. what is the independent and dependent variables? b. find the amplitude and the period of the function. c. create a trigonometric function that describes the hours of sunlight for each day of the year. d. graph the function you build in part c. e. use the function you build in part c to find out how many fewer daylight hours february 10 will have than march 21. you may look at the calendar.

The input to the function is x and the output is y. write the function such that x can be a vector (use element-by-element operations). a) use the function to calculate y(-1.5) and y(5). b) use the function to make a plot of the function y(x) for -2 ≤ x ≤ 6.