Which equation should you solve to find x? A. COS 26 = x/10
B. COS 26 = 9/10
C. Sin 26 = x/10
D. Tan 26 = 9/x

Choice C

sin(26) = x/10

Explanation:

With respect to the 26 degree angle, the x is the opposite side and the 9 is the length of the adjacent side.

We can say tan(26) = x/9 because tangent is the ratio of opposite over adjacent. In other words, tan(angle) = opposite/adjacent

Unfortunately, tan(26) = x/9 is not an answer choice.

Luckily though, we have other trig ratios to work with.

The sine ratio ties together the opposite side and hypotenuse

sin(angle) = opposite/hypotenuse

sin(26) = x/10

Extra info (optional section)

Solving for x leads to...

sin(26) = x/10

10*sin(26) = x

x = 10*sin(26)

x = 4.38371 approximately

Also, note how cos(26) = 0.89879 approximately, which is fairly close to 9/10 = 0.9. This indicates some rounding error is going on when your teacher is displaying either the 9, the 10, or the 26 degree angle.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: