Identify the correct trigonometry formula to use to solve for x.

Question

Answer 1

We know the adjacent and the angle, and we want to solve for the hypotenuse

adj / hyp = cos(55°)

11/x = cos(55°)

x = 11/cos(55°)

Answer 2

In relation to the 55 degree acute angle of the right triangle, the side with length 11 is the adjacent leg, the side with length x is the hypotenuse. By the way the other acute angle has a measure of 35 degrees. If you have learned the reciprocal trig ratios (secant, cosecant, cotangent), then there are 4 possible equations:

cos(55) = 11/x

sec(55) = x/11

sin(35) = 11/x

csc(35) = x/11

Let's use the 2nd equation above to solve for x:

sec(55) = x/11

x = 11 sec(55)

Using the 1st equation:

cos(55) = 11/x

x cos(55) = 11

x = 11/cos(55)

Visit this Desmos graph (by selecting the URL, right-clicking, and selecting "go to...") to see the results of solving all 4 equations for x.

desmos.com/calculator/ujrl0tefwc

Note that the wrench icon on this graph was used to set the calculator to degree mode.

x = 11sec(55)