From Page 544 in your book, you have: The area of a triangle equals one half the product of the lengths of any two sides and the sine of the angle between them. This means that for an arbitrary triangle with an interior angle θ, if sides of length a and b converge at an angle θ, then you have the formula: Area = 1/2
⋅a⋅b⋅sin(θ) Use the formula above to answer the following. Remember that the longest side is opposite the largest angle. Give exact answers. Decimal approximations will be marked wrong. Don't forget the degree symbol! (a) A triangle has side lengths 7 cm and 16 cm. If the angle between these two sides is 45 ^∘ , determine the area of the triangle. Area =×cm ^2
(b) An obtuse triangle has an interior angle 127 . If the two shortest sides have lengths 9 cm and 12 cm, determine the area of the triangle. Area =×cm ^2
(c) An obtuse triangle has an interior angle 113 ^∘ and area 144 cm ^2
. If the shortest sides have lengths 10 cm and b cm, determine b in cm. b=×cm