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What is the length of  AC ? Round to the nearest tenth.

A. 10.5 m

B. 12.3 m

C. 18.3 m

D. 21.4 m

What is the length of AC Round to the nearest tenthA 105 mB 123 mC 183 mD 214 m class=

Respuesta :

calculista

we know that

in the right triangle ABC

[tex]tan\ 55=\frac{opposite\ side\ angle\ 55}{adjacent\ side\ angle\ 55}[/tex]

in this problem

[tex]opposite\ side\ angle\ 55=BC=15m\\adjacent\ side\ angle\ 55=AC[/tex]

Substitute

[tex]tan\ 55=\frac{15}{AC}[/tex]

Solve for AC

[tex]AC=\frac{15}{tan\ 55}[/tex]

[tex]AC=10.5\ m}[/tex]

therefore

the answer is the option

A. 10.5 m

The measure of AC is 10.5 m which is in option A.

We have to determine

What is the length of the AC?

What is the tan angle?

The tangent is equal to the length of the side opposite the angle divided by the length of the adjacent side.

[tex]\rm Tan\theta = \dfrac{Perpendicular}{Base}[/tex]

Where the value of the perpendicular BC = 15m and [tex]\theta[/tex] = 55 degrees.

Therefore,

The measure of AC is;

[tex]\rm Tan\theta = \dfrac{Perpendicular}{Base}\\\\\rm Tan55 = \dfrac{15}{AC}\\\\1.42 = \dfrac{15}{AC}\\\\ AC = \dfrac{15}{1.42}\\\\AC = 10.5 m[/tex]

Hence, the measure of AC is 10.5 m which is in option A.

To know more about Tan angle click the link given below.

https://brainly.com/question/25342