Problem solving

Question

What is the area of the gable end of the house if it is a triangle with two sides being 42' that meet at a 105 deg angle ?

Answer 1

using the law of cosines first

x=the side opposite 105º angle

x²=42²+42²-2(42)(42)(cos[105])

x²=1764+1764-2(1764)(-0.258819)

x²=3528+913.1134

x²=4441.1134

x=66.64168

1/2(x)=33.32084

using the Pythagorean Theorem next

42²-(33.32084)²=h² where h is the height of the triangle

1764-1110.278=h²

653.7216=h²

h=25.5679

A=(1/2)(b)(h)

A=(1/2)(66.64168)(25.5679)

A=(1/2)(1703.888)

A=851.944 square feet