#### Question:

Unit 7 Right triangles and trigonometry homework one

Posted By Admin @ November 26, 2022

Unit 7 Right triangles and trigonometry homework one

Correct **responses**:

__x = √149____x = 4·√5____x = √(473)____x = √(191.93)____x = √(481)____x = 31 - 12·√2____x = 2·√(253)__

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:

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