Question

Unit 8 right triangle and trigonometry homework 5 trigonometry: finding sides and angles solve for x round to the nearest tenth.

Answer 1

Answer:

5. x = 25.6

6. x = 11.0

7. x = 41.8°

8. x = 64.2°

9. x = 12.8°

10. x = 51.3°

Step-by-step explanation:

Let's find the x value for each triangle.

For point 5      

We have:

x: is the opposite cathetus to 52°  

20: is the adjacent cathetus to 52°  

52°: is the angle

We can find "x" with the following trigonometric function:

$tan(52) = \frac{x}{20}$

$x = tan(52)*20 = 25.6$

For point 6      

We have:

x: is the hypotenuse  

5: is the opposite cathetus to the given angle  

27°: is the angle

To find "x" we need to use the trigonometric function:

$sin(27) = \frac{5}{x}$

$x = \frac{5}{sin(27)} = 11.0$

For point 7

We know:

x°: is the angle

6: is the hypotenuse

4: is the opposite cathetus to x°

Hence, x is:

$sin(x) = \frac{4}{6}$

$x = sin^{-1}(\frac{4}{6}) = 41.8$

For point 8    

We have:

x°: is the angle

14: is the adjacent cathetus to x°

29: is the opposite cathetus to x°

To calculate "x" we need to use the trigonometric function tan(x):

$tan(x) = \frac{29}{14}$

$x = tan^{-1}(\frac{29}{14}) = 64.2$

For point 9    

We have:

x°: is the angle

54: is the hypotenuse

12: is the opposite cathetus to x°

We can use sin(x) to solve for x:

$sin(x) = \frac{12}{54}$

$x = sin^{-1}(\frac{12}{54}) = 12.8$

For point 10  

We have:

x°: is the angle

40: is the hypotenuse

25: is the adjacent cathetus to x°

We need to use cos(x) to solve for x:

$cos(x) = \frac{25}{40}$  

$x = cos^{-1}(\frac{25}{40}) = 51.3$

I hope it helps you!