# Tutor profile: Hanna B.

## Questions

### Subject: Trigonometry

You are standing 8 feet away from the bottom of a building. The angle between the ground and the top of the building is 75 degrees. To the nearest foot, how tall is the building.

To solve this problem, we can draw a right triangle showing the building and where we are standing. We know that the base of this triangle is 8 ft, and the angle of elevation that we are standing at is 75 degrees. We can call the height of the building 'h'. To solve this problem, we will use the trig identity tan(theta) = opposite/adjacent. The height of the building is the opposite measurement and the 8 ft distance is the adjacent measurement. We would write tan(75)=h/8. To solve for h, we would multiply both sides by 8. 8tan(75)=h. We can then solve for h using a calculator and find that the height of the building to the nearest foot is 30 ft.

### Subject: Basic Math

Three-eighths of what equals 9? OR 3/8 of ____ = 9

In this problem we are given the part and we are asked to find the whole. We can divide 9 into three parts to find what 1/8 is equal to. 9 divided by 3 = 3, so 1/8 = 3. Now we can find what 8/8 (the whole) is equal to by multiplying 1/8 by 8. 3 x 8 = 24 so, 3/8 of _24_ = 9

### Subject: Algebra

Tom has 6 more than 3 times the amount of books that Jerry has. Together they have 18 books. How many books do each have?

To solve this problem we can write two equations. We will use the variable 'T' for the number of books that Tom has and 'J' for the number of books that Jerry has. The first sentence of the problem states that Tom has 6 more than 3 times the amount that Jerry has, so we would write the equation T = 6 + 3J. The second part of the problem states that together they have 18 books so we can write the equation T + J = 18. We can use substitution to solve this system of equations. First we can solve for J in the second equation to get J = 18 - T. Then we can plug this into the first equation to solve for T. When we plug it in we would get T = 6 + 3(18-T). Now we can simplify this equation to solve for T. T = 6 + 54 - 3T 4T = 6 + 54 4T = 60 T = 15, So Tom has 15 books. To find how many books Jerry has, we can plug this value into the second equation. 15 + J = 18 J = 3, So Jerry has 3 books.

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