Ok, so in other words, the decimal 0.1, is also known as 1/10. Because it is 1 tenth of one hundred, for the decimal place value. So, then you would want to multiply the 1/5 by 2, the top and bottom, numerator and denominator, by 2 to get it equal, or like terms, with 1/10. You would get 2/10. So, you are now looking for a number in between 1 and 2 with a denominator, or bottom number, of 100. To find that number, you will want to multiply the fractions, 1/10 and 2/10 by 10 get the denominator to 100. So, 1 times 10 is 10, and 10 times 10 is 100. So, you will end up with 10/100 for the first fraction and 20/100 for the second fraction. Then, you can make a fraction that has a whole number that is in between 10 and 20. I would pick 12, and then transfer that over to a decimal. So, it would become 0.12, since it is 12 percent, or 12 parts, of 100. <span />
Drawing a diagram of a triangle may be helpful. The hypotenuse is irrelevant, but the vertical leg and the horizontal leg are useful. Since we know the engineer is looking up at a 45 degree angle from a distance of 200 feet, we can label the vertical leg the "opposite", since it is on the opposite side of the angle we are given. The horizontal leg then becomes the "adjacent". You can then use trigonometry to solve for the opposite. The options are: sin(theta)= opposite/hypotenuse cos(theta)= adjacent/hypotenuse tan(theta)= opposite/adjacent Since we don't care about the hypotenuse, the last equation is the one to use. The angle we are given can be substituted in for theta: tan(45)= x/200 1.61977519= x/200 x= 323.955038 feet
