Answer:
DF = 3.0
<E = 31°
<F = 59°
Step-by-step explanation:
1. Use the Pythagorean Theorem to find side DF.
a² + b² = c²
5² + b² = 5.83²
25 + b² = 33.9889
b² = 8.9889
b = √8.9889
b = 2.998149429
b = 3.0
Side DF is equal to 3.0.
2. Use SOHCAHTOA to find the measure of <E. We know two sides: adjacent (5) and hypotenuse (5.83). So, we will use cosine.
Cosine = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{5}{5.83}[/tex] = 0.8576329331
Take the inverse cosine to find <E in degrees.
cos⁻¹ (0.8576329331) = 30.95 = 31°
<E is equal to 31°.
3. Add the two angles and subtract from 180° or use SOHCAHTOA to find the measure of <F.
90° + 31° + x = 180°
121° + x = 180°
x = 59°
or
We know two sides: adjacent (3.0) and hypotenuse (5.83). So, we will use cosine.
Cosine = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{3.0}{5.83}[/tex] = 0.5145797599
Take the inverse cosine.
cos⁻¹(0.5145797599) = 59.03063031 = 59°
<F is equal to 59°.
Hope that helps. :)
