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
