Answer:
x ≈ 36.09
Explanation:
Complete 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.
According to the diagram
m<E = 90 degrees
m<D = 49 degrees
DF = 55 = hypotenuse
DE = x = adjacent
EF = opposite
According to SOH CAH TOA identity;
Cos theta = adj/hyp
Cos m<D = DE/DF
Cos 49 = x/55
x = 55cos49
x = 55(0.6561)
x = 36.0855
x ≈ 36.09 (to the nearest hundredth)