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

36.08

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)=(x)/(55)`

To solve this, multiply both sides by 55:

`55* cos(49)=(x)/(55)* 55\\\\55cos(49)=x\\\\36.07=x`