In △jkl, solve for x.

(a)74.89
(b)30.29
(c)38.16
(d)66.73

ANSWER

(C)38.16

EXPLANATION

The acute angle given in the right triangle is 27°.

The side length adjacent to the 27° angle is 34 units.

The side length we want to find is x units, which is the hypotenuse of the right triangle.

We use the cosine ratio to obtain:

Solve for x,

to the nearest hundredth.

The correct answer is option C.  38.16

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

To find the value of x

From the figure we can see a right angled triangle. △JKL

Cos 27 = Adjacent side/Hypotenuse

 = KL/JL

 = 34/x

x = 34 / Cos 27

 = 34 / 0.891

 = 38.16

Therefore the correct answer is option C.  38.16