Using the figure below, if θ = 26° and y = 6, determine the exact value of x.
A)
B)
D)

Question

Using the figure below, if θ = 26° and y = 6, determine the exact value of x. 
A)​ 
B)​ 
D)​

Quizplus · Accepted Answer

Using trigonometry, we can set up the following equation:
tan(26°) = x/6
Simplifying and solving for x, we get:
x = 6tan(26°) ≈ 2.87
Since the question asks for the exact value of x, we must use the tangent addition formula:
tan(26°) = (tan(30°) - tan(4°))/(1 + tan(30°)tan(4°))
Simplifying and solving for x, we get:
x = 6(tan(30°) - tan(4°))/(1 + tan(30°)tan(4°)) = 6(√3 - 1/7)/(1 + √3/7) ≈ 5.55
Round to the nearest thousandth, we get x = 5.550. Therefore, the best choice is C.

Using the Figure Below, If θ = 26° and Y