Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.

1. First, you must calculate the height (h) of the triangle, as below:

Tan(α)=Opposite/Adjacent

α=30º
Opposite=16
Adjacent=h

2. When you substitute these values into Tan(α)=Opposite/Adjacent, you obtain:

Tan(α)=Opposite/Adjacent
Tan(30º)=16/h

3. Now, you must clear "h":

h(Tan(30º))=16
h=16/Tan(30º)
h=27.7

4. The value of "x" is:

Cos(β)=Adjacent/Hypotenuse

β=41º
Adjacent=h=27.7
Hypotenuse=x

5. When you substitute these values into Cos(β)=Adjacent/Hypotenuse, you have:

Cos(β)=Adjacent/Hypotenuse
Cos(41º)=27.7/x

6. You must clear "x", as below:

x(Cos(41º))=27.7
x=27.7/Cos(41º)

7. Therefore, the lenght "x" is:

x=36.70

skopie skopie · Answer 2 · 2019-07-17T04:42:38+02:00

Answer:

Step-by-step explanation:

Lets name the perpendicular drawn from vertex to opposite side " h " for calculation purposes (Refer the figure attached)

so first in the triangle ABC,

[tex]tan(30) = \frac{BC}{AC}[/tex]

[tex]tan(30) = \frac{16}{h}[/tex]

[tex]h= \frac{16}{tan(30)}[/tex]

[tex]h =16\sqrt{3}[/tex]

Now refer the triangle ACD , there we can use the trigonometric ratio

[tex]cos(41) =\frac{AC}{AD}[/tex]

[tex]cos(41) =\frac{16\sqrt{3} }{x}[/tex]

[tex]x =\frac{16\sqrt{3} }{cos(41)}[/tex]

x= 36.7