# Unit 7 right triangles and trigonometry homework 1 answer key

Posted By Admin @ November 26, 2022

#### Question:

Unit 7 Right triangles and trigonometry homework one

### Unit 7 Right triangles and trigonometry home work one

Correct responses:

1. x = √149
2. x = 4·√5
3. x = √(473)
4. x = √(191.93)
5. x = √(481)
6. x = 31 - 12·√2
7. 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)

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