The length of the hypotenuse of an isosceles right triangle is 15 feet. Solve for the length of the legs.
With trigonometry problems, the best first step is to draw out the triangle. Make an isosceles right triangle and write in the given information. Label the right angle and the two 45 degree angles, as well as the 15 foot hypotenuse. Since we don't know the length of the legs, label the two legs "x". Now the problem is all set up and we can solve for x. Pick any "x" and see that we have the hypotenuse and the angle opposite the leg (45 degrees). We can use the sin of 45 degrees to solve. Set up the equation: Sin45 = x / 15. Multiply both sides by 15 and use a calculator to solve for x. (Make sure the calculator is on degree mode!). x = 10.6. The legs are both 10.6 feet long. Alternatively, we could have used the Pythagorean Theorem. 2x^2 = 15^2, and x = 10.6.
It's Friendship Day and Jimmy wants to gift his friends some candy. He has 32 pieces of candy. Jimmy gives 1/4 of his candy to Josh, 3/16 to Rob and 1/2 to Chris. How much candy does Jimmy have left?
This question is all about working with fractions. A good way to think about fractions in the beginning is to imagine the total amount (32 pieces of candy) divided into the number of sections in the denominator (bottom number). Let's think about how much candy Josh gets first. Jimmy gives Josh 1/4 of his candy, so let's split 32 pieces into 4 different parts. 32/4 = 8, so 4 sections of 8 pieces of candy each. The numerator (top number) is 1, so Josh gets 1 of these sections- Josh gets 8 pieces. Let's follow the same procedure for Rob. 32/16 = 2, or 16 sections of 2 pieces each. The numerator is 3, so Rob gets 3 of these sections, or 6 pieces. Now for Chris- 32/2 = 16, 16 x 1 = 16. Chris gets 16. How many does Jimmy have left? 32- (8 + 6 + 16) = 2. Jimmy has 2 pieces of candy left.
Manny and his parents go to a concert and their tickets cost a total of $40. Manny's ticket is $8. How much does one adult ticket cost?
The best way to approach these problems is to think about what you know and what you're looking for. You know that Manny's ticket cost $8, and that Manny's ticket and 2 adult tickets cost $40. You're looking for the price of one adult ticket. Let's set up an algebraic equation to represent this. Since you don't know the price of one adult ticket, represent that value with "x". Manny's ticket + two times the cost of one adult ticket = $40. --> 8 + 2x = 40. Solve for x by subtracting 8 from both sides. 2x = 32. Divide both sides by 2. x = 16. The price of one adult ticket is $16.