Respuesta :
Unit 7 Right triangles and trigonometry home work one
Correct responses:
- x = √149
- x = 4·√5
- x = √(473)
- x = √(191.93)
- x = √(481)
- x = 31 - 12·√2
- x = 2·√(253)
Which methods can be used to find the value of x?
The value of x can be found by using Pythagorean theorem
Base on images of the right triangles in the Unit 7 Right
triangles homework, we have;
1. The lengths of the legs of the right triangles are;
10 and 7
According to Pythagorean theorem, the hypotenuse, x, is given as follows;
- x = √(10² + 7²) = √149
2. The length of the hypotenuse = 21
Length of the a leg = 19
- Length of the second leg x = √(21² - 19²) = √(80) = 4·√5
3. Length of the hypotenuse = 27
Length of a leg = 16
Therefore;
- x = √(27² - 16²) = √(473)
4. Length of the legs are; 12.8 and 5.3
Therefore;
- Length of the hypotenuse, x = √(12.8² + 5.3²) = √(191.93)
5. The two triangles formed by the perpendicular to the side
with length 18 are similar according to Side-Angle-Side
similarity postulate.
Therefore;
The perpendicular line is a perpendicular bisector to the side
having a length of 18 (divides the segment into two).
The leg lengths of the right triangle that has x as the
hypotenuse side are; 9 and 20
Therefore;
- x = √(20² + 9²) = √(481)
6. The given figure is an isosceles trapezoid.
The base length, l, of the right triangle that has 19 as the
length of the hypotenuse side is; l = √(19² - 17²) = √(72) = 6·√2
According to the properties of an isosceles trapezoid, the
base length of the two right triangles are congruent.
Length of x = 31 - The base length of the two right triangles
Which gives
Therefore;
- x = 31 - 2 × 6·√2 = 31 - 12·√2
7. Height of the triangle, h = √(22² - 16²) = √(228) = 2·√(57)
The height of the triangle is a leg of the right triangle that has
x as the length of the hypotenuse side.
The other leg length = 44 - 16 = 28
Therefore;
- x = √(28² + (2·(√57))²) = √(28² + 228) = 2·√(253)
Learn more about Pythagorean theorem here:
https://brainly.com/question/24481277
