The height to the base of an isosceles triangle is 12.4m, and its base is 40.6m. What are the measurement of the angles of the triangle and the length of its legs?

Answer:Base Angles=31.42°Length of legs=23.79 mVertex 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 anglesBase angles can be solved by using the tan of one of the base angles, let the base angle be ∅.Using the formula Tan∅=opposite/adjacentWhere the opposite side=Height=12.4 m, and the adjacent side=0.5×Base length= 0.5×40.6=20.3 mTan∅=12.4/20.3=0.61∅=(Tan∧-1)×0.61=31.42°Base angle=31.42°   2. Length of legsThe length of each of the legs can be g the formulaHypotenuse=√((Height)²+(0.5×base length)²)=√(12.4²+20.3²)=23.79 mLength of the legs=23.79 m3. Vertex angleLet the vertex angle be xTotal angles in a triangle should add up to 180°, meaning(2×base angle)+vertex angle=180°(2×31.42°)+x=180°62.84+x=180x=180-62.84=117.16°Vertex angle=117.16°