Practice Problems
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Amoagh-
1.Tell weather each triangle is a 30-60-90 triangle or a 45-45-90 or neither.
a)This is a 30-60-90 triangle. The hypotenuse is double the shorter leg which is 3 and 3 times 2 is 6. Also the longer leg is square root of 3 times the shorter leg of the triangle.
1.Tell weather each triangle is a 30-60-90 triangle or a 45-45-90 or neither.
a)This is a 30-60-90 triangle. The hypotenuse is double the shorter leg which is 3 and 3 times 2 is 6. Also the longer leg is square root of 3 times the shorter leg of the triangle.
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b)This is neither. This is an isosceles triangle, but the hypotenuse doesn't follow the rule. It isn't a leg multiplied by the square root of 2, but instead it was multiplied by the square root of three.
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c)This is a 45-45-90 triangle. It has two equal legs along with a hypotenuse with a value of square root of 2 and 12.
2.Find the perimeter of rectangle ABCD. This is an isosceles trapezoid.
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You first find the shorter legs of the triangle. It is 2 because 8-4=4 and then divide it by 2. After that you use that to find segment AC by multiplying 2 by square root of 3 and you get 2 square root of 3. After that you use that and multiply 2 square rot of 3 by 2 and add it to 4 multiplied by 2. You get 4 square root of 3 plus 16 as the answer.
Amer-
1) If BF is equal to √96, AB is 8, and AD is 6 then what is the length of AG?
1) If BF is equal to √96, AB is 8, and AD is 6 then what is the length of AG?
By using the equation of squaring the length, width, and height and adding them together, it has a sum of the cube's hypotenuse squared. From this, we can get 96+64+36 = AG^2 or 196 = AG^2. Then, the square root of 196 is equal to 14, the length of segment AG.
Amer-
2) Find the length of the base of an isosceles triangle whose perimeter is 128 with an altitude of 16.
2) Find the length of the base of an isosceles triangle whose perimeter is 128 with an altitude of 16.
Since the triangle is an isosceles triangle with an altitude of 16, the first step is to find a Pythagorean triple that would add up to 80, because half of the perimeter is each right triangle and the altitude is 16 of the 80, making it 64. The triple that works in the situation is 16-30-34, making the perimeter 128 with 2 legs and 2 hypotenuses. The length of the base would become 60.
A man is 6 feet tall. He is standing on the ground, looking at a pole in the sky with a telescope. The base of the pole is 54 feet away from the man. The top of the pole is 90 feet away from the man. How tall is the pole?
Ans: 78 Explanation: First, since it is a right triangle, you use the Pythagorean Theorem. So, you do 90^2-54^2= top part of the pole. After solving it, you get 72 as the length. Next, you add 6 to 72 because the man is 6 feet tall. Therefore, the answer to this question is 78. Submitted by Andy Liu. |
Find x.
Ans: 2 sqrt(3) Explanation: First, since the first triangle is a 45-45-90 triangle, you multiply 3 by sqrt(2) to find the hypotenuse of the 45-45-90 triangle to get 3 sqrt(2). Next, since you know that the middle triangle is a 30-60-90 triangle, you divide 3 sqrt(2) by sqrt(3) to get the length of the side of the square. The answer to that is sqrt(6) because doing 3 sqrt(2) divided by sqrt(3) equals to 3 sqrt(6) divided by 3 which simplifies into sqrt(6). After getting the side of the square, you multiply it by sqrt(2) because the diagonal and the sides of a square form a 45-45-90 triangle. sqrt(2) times sqrt(6) equals to sqrt(12), which simplifies into 2 sqrt(3). This is because 12 is equal to 2^2 *3, so you can factor out a 2. Therefore, the answer to this problem is 2 sqrt(3). Submitted by Andy Liu. Adarsh
Charlie is challenged by his friend to find out how high above the ground the top of the kite is when he is flying it. Charlie is told that the kite is 3 feet tall, and the string is 72 feet long. He is also told that the right triangle formed in the kite string, ground, and altitude, will be a 45-45-90 triangle, and that Charlie is 5 feet tall. How to solve First, we must find the vertical height of the kite string. To do this we use a key formula in 45-45-90 triangles, which states that the hypotenuse and legs are in a ratio of sqrt2 and 1, respectively. So to solve this question, we divide 72 by the square root of 2. This equals roughly 51. Now we must add the height of the kite. 51+3=54, which after adding Charlie's height of 5 feet, gives us our final answer of 59 feet above the ground. Adarsh Mary is walking to her friend's house. She usually takes a long route, in which she heads 5 miles east and twelve miles north. However, after learning geometry in Mrs. Ashmore's class, she decided she would find a shorter path to her friend's house. However, while she set to work solving for a quicker route she suddenly realized that she forgot to watch the Edward Burger videos! Help Mary find the quickest route! How to solve The first step is to identify that the 5 miles east and 12 miles north can be used as the sides to a right triangle. After identifying this, we can use the Pythagorean theorem to find the answer. This theorem states that for any right triangle, the formula: a^2+b^2=c^2 can be used to find the length of the hypotenuse. Lets plug in the numbers. 5^2+12^2=c^2. This equals 25+144=c^2. This simplifies to 169=c^2. The square root of 169 is 13. Equation solved!. Now we know that the fastest rout is along the hypotenuse and is exactly 13 miles long |