# Tutor profile: Caroline H.

## Questions

### Subject: Geometry

The side lengths of a right triangle are 3in, 4in, and 5in. Provide the Sine (sin), Cosine (cos), and Tangent (tan) of angle (<) A and <B, given that <A is greater than <B. Leave answers are fractions.

Using the pneumonic device SohCahToa (sin=opposite/hypotenuse; cos=adjacent/hypotenuse; tan=opposite/adjacent), I can find the sin, cos, and tan of each angle using the given side lengths. First, I need to know what side lengths are the opposite, adjacent, and hypotenuse of <A. I know that the hypotenuse of any right triangle is going to be the longest length, so the hypotenuse is 5in. Because I know that <A is greater than <B, so the opposite side of <A is the greatest leg length, so the opposite of <A is 4 in. This means that the adjacent leg length to <A is 3in. sin(A)=opp/hyp=4/5 cos(A)=adj/hyp=3/5 tan(A)=opp/adj=4/3 Next, I’ll focus on <B. Because <B is smaller than <A, the shortest leg of the triangle (3in) is opposite of <B. That means the adjacent leg is 4in. The hypotenuse of 5in remains the same. sin(B)=opp/hyp=3/5 cos(B)=adj/hyp=4/5 tan(B)=opp/adj=3/4

### Subject: Environmental Science

What are the top 3 causes of species endangerment? Using an example, show how these causes impact species.

1) Habitat Loss and Fragmentation: All species on earth need a place to live that is suitable to their needs. Just like humans, all species (animal or plant) need water, nutrients, and shelter. When a species' habitat is destroyed or broken into pieces, it limits the species ability to attain the water, nutrients and shelter it needs to survive. For example, the American Bison, or Buffalo, use to roam the expanse of United States praise land (most of the middle part of the country). Now, because there is so much human development and different land management techniques, the American Bison is limited to small patches of preserved prairie land set aside by humans. The loss of wide expanses of prairie land has created a serious risk that Bison, without the continued help from humans, will become extinct. 2) Overhunting / Predation: When a species is overhunted by humans or other predators, there is the possibilities that the species will become endangered. American Bison were subject to endangerment when European began to settle in North America and move across the continent from East to West. Because certain body parts of the Bison, like the tongue and hide, were seen as valuable, Bison were slaughtered by the hundreds. Over a relatively short span of years, the Bison population was decimated Bison are now considered ecologically extinct, meaning that there are not enough Bison in a wild habitat to continue the species without help from humans. 3) Invasive Species: Invasive species are typically a species of plant or animal that has been introduced to an area and is impacting a native species ability to survive. American Bison are Native to the Central Plains/ prairie region of North America. However, Bison have been relocated to other parts of the country, where they have become an invasive species. The ecological impact of Bison in their natural habitat often aids the surrounding plants with seed dispersal. However, in a habitat in which they have been introduced, they often cause significant damage to local vegetation by eating and trampling it.

### Subject: Algebra

Given the points (3,2) and (6,8) on a coordinate grid, provide the equation of a line in slope-intercept form.

For slope-intercept form (y=mx+b), you need to find slope (m) and the y-intercept (b). The slope formula for 2 points is m=(y2-y1)/(x2-x1). Using the points given, m=(8-2)/(6-3)=6/3=2. The slope is up 2 units and right 1 unit. Using the slope and one of the given points (3,2), I can find the y-intercepts: y=mx+b (plug in known variables) 2=2(3)+b (peMdas- multiply) 2=6+b (subtract 6 on both sides to get b by itself) -4=b The equation of the line: y=mx+b (plug in slope (m) and y-intercept (b)) y=2x+(-4)