Question

The equation cos−1 = x can be used to determine the measure of angle BAC.

Answer 1

we know that

in the right triangle ABC

the value of cosine of angle x is equal to

$cos(x)=\frac{AC}{AB}$

we have

$AC=3.4\ cm\\AB=10\ cm$

substitute the values

$cos(x)=\frac{3.4}{10}=0.34$

Find the measure of angle x

$x=cos(x)^{-1} =arc\ cos(0.34)=70.12\°$

Round to the nearest whole degree

$x=70\°$

therefore

the answer is

$70\°$

Answer 2

The value of $\boxed{\angle BAC=x=70^\circ }$ .

Further explanation:

Given:

The given right angle triangle is $\Delta ABC$ .

The length of $AC$  is  $3.4{\text{ cm}}$, the length of $AB$  is ${\text{10 cm}}$  and $\angle BAC=x$ .

Step by step explanation:

Step 1

Now the base of $\Delta ABC$  is $AC$  and the hypotenuse is $AB$  corresponds to angle $x$ .

The value of cosine of angle $x$  can be represented as,

$\cos\left(x\right)=\frac{{AC}}{{AB}}$                                                                              ……(1)

Since the values are $AC=3.4{\text{ cm, }}AB=10{\text{ cm}}$ .

Now substitute the values $AC=3.4{\text{ cm, }}AB=10{\text{ cm}}$  in equation (1).

$\begin{aligned}\cos\left(x\right)&=\frac{{3.4}}{{10}}\\&=0.34\\\end{aligned}$

Step 2:

Now find the inverse of the cosine to obtain the value of $x$  as,

  $\begin{gathered}x={\cos^{-1}}\left({0.34}\right)\hfill\\x=70.12^\circ\hfill\\\end{gathered}$

Step 3:

Now round the value of $x$  to the nearest whole degree.

   $x=70^\circ$

Therefore, the value of $\angle BAC=x=70^\circ$ .

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Trigonometry

Keywords: Cosine function, sine function, equation, inverse, angle, round, whole degree, value, trigonometry, right angle triangle, perpendicular, base, hypotenuse