Answer:
Base Angles=31.42°
Length of legs=23.79 m
Vertex angle=117.16°
Step-by-step explanation:
An isosceles triangle is a triangle whose leg lengths are equal. They also form base angles that are equal.
Base angles can be solved by using the tan of one of the base angles, let the base angle be ∅.
Using the formula Tan∅=opposite/adjacent
Where the opposite side=Height=12.4 m, and the adjacent side=0.5×Base length= 0.5×40.6=20.3 m
Tan∅=12.4/20.3=0.61
∅=(Tan∧-1)×0.61=31.42°
Base angle=31.42°
2. Length of legs
The length of each of the legs can be g the formula
Hypotenuse=√((Height)²+(0.5×base length)²)=√(12.4²+20.3²)=23.79 m
Length of the legs=23.79 m
3. Vertex angle
Let the vertex angle be x
Total angles in a triangle should add up to 180°, meaning
(2×base angle)+vertex angle=180°
(2×31.42°)+x=180°
62.84+x=180
x=180-62.84=117.16°
Vertex angle=117.16°
