# Tutor profile: Elizabeth K.

## Questions

### Subject: Trigonometry

If a triangle has angles measuring 25 $$ ^\circ $$ and 28 $$ ^\circ $$ and the length of the side opposite the angle measuring 28 $$ ^\circ$$ is 10 feet, what are the lengths of the other two sides?

First we can use the law of sines to find the answer. $$ a/sinA = b/sinB =c/sin C$$ Let $$ a = 10$$. Then $$A=28$$. Side opposite the angle. Let $$ B=25$$. And since the sum of the angles of a triangle must equal 180, then $$ A+B+C =180$$ $$ 28+25+C=180$$ $$ 53 +C = 180$$ $$ C= 127$$ Let's find side $$b$$ first. $$ a/sinA = b/sinB $$ $$ 10/ sin(28) = b/sin(25)$$ $$ 9 = b$$ Now side $$c$$. $$ a/sinA=c/sinC$$ $$10/sin(28)=c/sin(127)$$ $$17 = c$$ The sides of the triangle are 17, and 9 feet.

### Subject: Pre-Algebra

The sum of three consecutive numbers is 72. What are the numbers?

Since the numbers are consecutive, it means that they follow each other. For example, 5,6, and 7 are three consecutive numbers. Let the first number be $$x$$. Then second number is one greater or $$x+1$$. And the third number is $$ x +2$$ or two greater than the first. These three numbers must add up to 72. Add up the three numbers and set them equal to 72. $$x + (x+1) + (x+2) =72$$ Simply. $$ 3x + 3 =72$$ Now find $$x$$. $$ 3x = 72-3 = 69$$ $$ 3x/3=69/3$$ $$x = 33$$ Therefore the numbers are 33, 34, and 35.

### Subject: Algebra

Sue and Dave buy some fruit. Sue buys 5 apples and 2 bananas for $2. Dave buys 2 apples and 3 bananas for $1.35. Find the cost of one apple and one banana.

Let $$ a =$$ one apple. Let $$ b=$$ one banana. Convert $2 to 200 cents and $1.35 to 135 cents. Sue buys $$ 5 a + 2 b = 200$$ Dave buys $$ 2 a + 3 b = 135$$ Now we can solve this set of simultaneous equations. Multiply the first equation by 3 and the second by 2. $$ 15 a + 6 b = 600$$ $$ 4 a + 6 b = 270 $$ Next subtract the second equation from the first. $$ (15-4) a + (6-6) b = (600-270)$$ $$ 11 a + 0 b = 330 $$ $$ 11 a = 330 $$ Solve for $$a$$ by dividing both sides of the equation by 11. $$ 11/11 a = 330/11 $$ $$ a = 30$$ Now find $$b$$ by substituting $$a$$ back into the first equation. $$ 5 (30) + 2 b = 200$$ $$ 150 + 2 b = 200$$ Solve for $$b$$. $$ 2 b = 200-150$$ $$ 2 b = 50$$ $$ b = 50/2 = 25$$ Therefore $$ a = 30 $$ cents$$ = $0.30$$ = cost of one apple $$ b= 25$$ cents $$= $0.25$$ = cost of one banana

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