# Tutor profile: Michael E.

## Questions

### Subject: Trigonometry

A woman on the ground level is looking at the top cliff of the building with an angle of elevation of 40 degrees. She knows that the height of the building is 300 feet. She wants to know how far is she from the ground level of that building. How will you help her finds her distance from that building?

We can calculate her distance from the ground floor of the building using the trigonometric ratios. Tangent 40 = 300 ft / x where x is the distance from her position to the ground level of the building. 0.83909963 = 300 ft / x x = 300 ft / 0.83909963 x = 357.53 ft (answer)

### Subject: Geometry

A rectangle has a width of 5 cm and a diagonal of 10 cm. 1. What is the length of the rectangle? 2. What is the area of the rectangle?

1. Given: Width = 5 cm, Diagonal = 10 cm To find the length of the rectangle, we can use Pythagorean Theorem. Square of the Length = square of the diagonal (10 cm)^2 minus square of the width (5 cm)^2 Length = square root of [ 100 cm^2 - 25 cm^2] Length = square root of 75 cm^2 = 8.66 cm (answer) 2. The area of the rectangle is equal to the product of its length and width. Area = length x width Area = 5 cm x 8.66 cm Area = 43.3 cm^2 (answer)

### Subject: Algebra

Let f(x) = 2x + 3. Graph f and h. Describe the transformation from the graph of f to the graph of h. 1. h(x) = f(x) + 3 2. h(x) = −f(x) - 1

1. The graph of h is vertically translated 3 units up from the graph of f. 2. The graph of h is reflected and vertically translated 1 unit down from the graph of f.

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