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Rowena-renee X.
Mathematics Coach with over 5 years Teaching/Tutoring Experience
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Trigonometry
TutorMe
Question:

In a right triangle ABC with angle A equal to 90 degrees, find angle B and C so that sin(B) = cos(B).

Rowena-renee X.

Assign variables: h - hypotenuse b - side opposite angle B c - side opposite angle C Then: $$sin(B) = \frac{b}{h}$$ $$cos(B)= \frac{c}{h}$$ Since we want $$sin(B)=cos(B)$$ Then $$\frac{b}{h}$$ must be equal to $$\frac{c}{h}$$ Therefore if $$\frac{b}{h}=\frac{c}{h}$$ Then $$b = c$$ And triangle ABC is an isosceles right triangle making angles B and C 45 degrees each since the sum of the interior angles of a triangle is 180 degrees and angle A is 90 degrees.

Geometry
TutorMe
Question:

Angles A and B are complementary and the measure of angle A is twice the measure of angle B. Find the measures of angles A and B.

Rowena-renee X.

Complementary angles sum to 90 degrees, so: $$A + B = 90$$ And A is TWICE B so: $$A=2B$$ Using the method of substitution: $$2B+B=90$$ $$3B=90$$ $$B=\frac{90}{3}$$ $$B=30$$ And A: $$A=2B$$ $$A=2(30)$$ $$A=60$$ Therefore B is 30 degrees and A is 60 degrees.

Algebra
TutorMe
Question:

Alyssa dumped 9 lbs of a bag of apples with 46 % red apples, into a bag of 11 lbs which contained 40 % red apples. What is the new percent of red apples?

Rowena-renee X.

Let's simplify: 9 lbs of 46% red apples PLUS 11 pounds of 40% red apples IS EQUAL to (9+11) lbs of A CERTAIN percent of apples So: $$9(0.46)+11(0.40)=20(x)$$ $$4.14+4.4=20x$$ $$8.54=20x$$ $$\frac{8.54}{20}=x$$ $$0.427=x$$ Thus the new percent of red apples is $$42.70\%$$

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