Question

Use △DEF, shown below, to answer the question that follows: Triangle DEF where angle E is a right angle. DE measures x. DF measures 55. Angle D measures 49 degrees. What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.

Answer 1

so is it 36.07 or 36.08

Answer 2

Answer:

36.08

Step-by-step explanation:

Side DE is the side adjacent to ∠D.  Side DF is the hypotenuse of the triangle.  Adjacent/hypotenuse is the ratio for cosine; this gives us the equation

$\cos{49}=\frac{x}{55}$

To solve this, multiply both sides by 55:

$55\times \cos{49}=\frac{x}{55}\times 55\\\\55\cos{49}=x\\\\36.07=x$