Answer:
11.8 cm²
Explanation:
Cosine rule: a ² = b ² + c ² - 2bc COS A
COS A = (b ² + c ² - a ²) / (2bc)
Area of triangle = ½ ab sin C
name the angle that joins the '3' side to either of the '8' sides. label that angle as A.
now, Cos A = (8² + 3² - 8²) / [(2)(3)(8)]
= 3/16.
A = inverse Cos (3/16)
= 79.193°.
Area of triangle = 1/2 ab Sin C (we'll just use letter A instead of C)
= 1/2 (3)(8) sin (3/16)
= 11.8 cm².
another way you can find it is by this simpler method:
think of one side of 8, the side of 3 and the height that you do not know by using Pythagoras' Theorem for right-angled triangle. (a² + b² = c²). go halfway up the '3' side, then cut across straight to where the '8' sides meet. we now have right-angled triangle. let's call the height you don't know h.
we have 1.5² + h² = 8²
h² = 8² - 1.5²
h² = 61.75
h = √61.75
so area = 1/2 X 1.5 X √61.75
= 11.8 cm²