In a right triangle ABC with angle A equal to 90o, find angle B and C so that sin(B) = cos(B).
Let b be the length of the side opposite angle B and c the length of the side opposite angle C and h the length of the hypotenuse. sin(B) = b/h and cos(B) = c/h sin(B) = cos(B) means b/h = c/h which gives c = b The two sides are equal in length means that the triangle is isosceles and angles B and C are equal in size of 45o.
Add the following fractions: 1/3 + 3/5
Find a common denominator: 3*5 = 15 Multiply top and bottom of 1/3 by 5: 5/15 Multiply top and bottom of 3/5 by 3: 9/15 Rewrite: 5/15 + 9/15 Add numerators (top): 5+9 = 14 Keep denominator (bottom): 14/15 Answer 14/15.
Simplify the expression 2(a -3) + 4b - 2(a -b -3) + 10
Distribute: 2a - 6 + 4b - 2a +2b + 6 + 10 Group Like Terms: 2a - 2a + 4b + 2b - 6 + 6 + 10 Simplify: 0a + 6b + 10 Answer: 6b + 10