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Kristina O.

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Trigonometry

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Question:

We have a triangle. One of the angles on the triangle is 20 degrees. The length of the side that is opposite of the angle is 65. The length of the hypotenuse and the adjacent side are both unkown. Find the length of the hypotenuse.

Kristina O.

Answer:

We should draw the triangle and think of SOH-CAH-TOA. This means that you find the angle using either: SOH which is $$sin(\alpha)=O/H$$ or CAH which is $$cos(\alpha)=A/H$$ or TOA which is $$tan(\alpha)=O/A$$ In this case: $$\alpha=20$$, O=65, A=unkown, and H=unknown. Since we only know $$\alpha$$ and O and we are looking for H, we should use $$sin(\alpha)=(O/H)$$ to solve. Plug in the numbers: $$sin(20)=65/H$$ or $$H=65/sin(20)$$ Solve for H by plugging into the calculator. The answer should be 190.047. If your answer was 71.198, you should check the mode on your calculator. The mode should be set to DEGREES, not radians.

Basic Math

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Question:

Solve: $$3+(10-6)+5*2$$

Kristina O.

Answer:

We need to use PEMDAS to know the order in which to solve this. PEMDAS stands for parenthesis, exponents, multiplication, division, addition, subtraction. Let's begin: Parenthesis: $$(10-6)=4$$ Now we have $$3+4+5*2$$ Exponents: none Multiplication: $$5*2=10$$ Now we have $$3+4+10$$ Division: none Addition: $$3+4+10=24$$ . We solved it!

Algebra

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Question:

Please factor the following trinomial: $$3x^(2}+4x-15$$

Kristina O.

Answer:

(Step 1): Look at this as $$ax^{2}+bx+c$$ . We need to find a way to break down bx into two numbers. These two numbers should add up to b, but when multiplied it should equal the same number as when you multiply a and c. In this case, b is 4 and the product of a and c is -45. 9 and (-5) would add up to 4 and when multiplied, it equals -45. (Step 2): Rewrite with bx broken down: $$3x^{2}+9x-5x-15$$ (Step 3): Factor the GCF for each side of the equation: GCF for $$3x^{2}+9x$$ is 3x and GCF for $$-5x-15$$ is -5 (Step 4): Rewrite with GCF factored out of each pair: $$3x(x+3)-5(x+3)$$ (Step 5): Distributive Property - pair the GCF and drop the matching binomial in the parenthesis like so: $$(3x-5)(x+3)$$

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