In the triangle below, determine the value of a.

Step-by-step explanation:

This is classic right triangle trig.  Side a, our unknown, is adjacent to angle C which is a given.  You always have to use a given angle and side to find a missing side, so we have to figure out how the two givens are related to our unknown.  Side a is adjacent to angle C, and we are also given the hypotenuse.  We know side a is not the hypotenuse since the hypotenuse is ALWAYS the side across from the 90 degree angle.  The tan ratio of angle C will give us a way to have only one unknown.

tan 43 = a/26 and

26 tan 43 = a

Use your calculator now to find the missing side.  

a = 24.2 units long

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

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