Use the Law of Cosines to indicate side c if a=3.0, b=4.0, angle C=53deg.
Since we are given the measure of side 'a' and 'b', then we will need to find side 'c' using the formula: (c^2) = (a^2) + (b^2) - 2ab * cos(C) First, we plug in what is given (c^2) = (3.0^2) + (4.0^2) - 2(3.0)(4.0) * cos(53 deg) Next, solve for each exponent (c^2) = (9) + (16) - 2(3.0)(4.0) * cos(53 deg) Then, multiply (c^2) = (9) + (16) - 24 * cos(53 deg) Solve for cosine (c^2) = (9) + (16) - 24 * 0.60 Finally, solve the right hand side of the equation to get (c^2) = 10.6 To get the final answer, solve for c by square rooting both sides of the equation to get c = sq.rt(10.6) c = 3.3 Therefore, the length of side 'c' is about 3.3
A farmer wants to fence a field that is in the shape of a right triangle. He knows that the two shorter sides of the field are 20 yards and 35 yards long. How long will the fence be to the nearest hundredth of a yard?
Since the fence is in a shape of a right triangle and we are given two of the shorter lengths, we need to find the third length, which is the hypotenuse. To find this, we need to use the Pythagorean Theorem. The formula for the Pythagorean Theorem is (a^2)+(b^2)=(c^2). Since we are given the two shorter lengths, this will be plugged in for 'a' and 'b' in our formula as follows: (a^2)+(b^2)=(c^2) (20^2) + (35^2) = (c^2) We need to solve for 'c'. So, 400+1225=(c^2) Add 1625 = (c^2) Square root both sides to get sq.rt(1625) = c We need to round this to the nearest hundredth, so the answer will be c = 40.31 Now that we know all sides of the right triangle (20, 35, 40.31), we can find how long the fence will be by finding the perimeter of the triangle. This will be done by adding all of the sides together. P = a+b+c P = 20+35+40.31 All all sides P = 95.31 Therefore, the fence will be about 95.31 yards long.
Find an equation that is perpendicular to x+5y=50 and passing through the point (5,10).
To find an equation that is perpendicular to the one given, we must use the point-slope formula, which is y-y1=m(x-x1). We have what (x1,y1) is, which is given as (5,10). Before we can start plugging into the formula, we need to find the slope. To find the slope we use the equation that is given x+5y=50. We need to arrange this equation so that it is in the form y=mx+b. In other words, solve for y. To do so, we can subtract x on both sides of the equation, which gives 5y= -x+50. Then, to get y alone on the left hand side, we need to divide 5 on both sides of the equation. The result is y= -(x/5)+(50/5), which can be simplified to y= -(x/5)+10. The slope for this equation is -(1/5), which we need to change to the opposite and reciprocal, since the equation we need to find is perpendicular. If we were finding an equation that is parallel, we would use the same slope as the equation given. So, in this case, our slope or the 'm' in our formula will be equal to 5. Now that we have the slope, and our (x1,y1) point, we can finally use the point-slope formula to find the new equation. It will be plugged in as: y-y1=m(x-x1) y-10=5(x-5) First, distribute the 5 y-10=5x-25 Then, add 10 to both sides of the equation to get your final answer y=5x-15