find $m\\angle e$.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$m\\angle…

find $m\\angle e$.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$m\\angle e = \\square ^\\circ$

find $m\\angle e$.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\n$m\\angle e = \\square ^\\circ$

Answer

Explanation:

Step1: Identify sides relative to ∠E

In right triangle (EGF), (\angle G = 90^\circ):

  • Opposite side to (\angle E): (GF)
  • Adjacent side to (\angle E): (EG = 4)
  • Hypotenuse: (EF = 10) First, calculate (GF) using Pythagorean theorem: $$GF = \sqrt{EF^2 - EG^2} = \sqrt{10^2 - 4^2} = \sqrt{100 - 16} = \sqrt{84} \approx 9.165$$

Step2: Use cosine to find ∠E

Cosine of (\angle E) is ratio of adjacent to hypotenuse: $$\cos(\angle E) = \frac{EG}{EF} = \frac{4}{10} = 0.4$$ Calculate (\angle E) using arccosine: $$\angle E = \arccos(0.4) \approx 66.4^\circ$$

Answer:

(66.4)