2) If AB ≅ EB, then ∠BAE ≅ ∠BEA
4) If ∠EBC ≅ ∠ECB, then EB ≅ EC
6) x = 60
8) x = 20
13) y = 5
x = 30°
What are the lengths and angles of the triangle?
2) If AB ≅ EB, then ∠BAE ≅ ∠BEA
4) If ∠EBC ≅ ∠ECB, then EB ≅ EC
6) Using law of sine, we can find the length of x as:
x/sin 60 = 60/sin 60
x = 60/1
x = 60
8) This is an equilateral triangle because all sides are equal. The inteorior angles are each 60 degrees.
Thus:
3x = 60
x = 20
13) Using law of sines again:
8y/sin 60 = 40/sin 60
8y = 40
y = 5
Using Pythagoras theorem we can find the base of the triangle as:
z = √(80² - 40²)
z = 69.282
Thus:
69.282/sin 120 = 40/sin x
sin x = (40 * sin 120)/69.282
sin x = 0.5
x = sin⁻¹0.5
x = 30°