The value of [tex]\boxed{\angle BAC=x=70^\circ }[/tex] .
Further explanation:
Given:
The given right angle triangle is [tex]\Delta ABC[/tex] .
The length of [tex]AC[/tex] is [tex]3.4{\text{ cm}}[/tex], the length of [tex]AB[/tex] is [tex]{\text{10 cm}}[/tex] and [tex]\angle BAC=x[/tex] .
Step by step explanation:
Step 1
Now the base of [tex]\Delta ABC[/tex] is [tex]AC[/tex] and the hypotenuse is [tex]AB[/tex] corresponds to angle [tex]x[/tex] .
The value of cosine of angle [tex]x[/tex] can be represented as,
[tex]\cos\left(x\right)=\frac{{AC}}{{AB}}[/tex] ……(1)
Since the values are [tex]AC=3.4{\text{ cm, }}AB=10{\text{ cm}}[/tex] .
Now substitute the values [tex]AC=3.4{\text{ cm, }}AB=10{\text{ cm}}[/tex] in equation (1).
[tex]\begin{aligned}\cos\left(x\right)&=\frac{{3.4}}{{10}}\\&=0.34\\\end{aligned}[/tex]
Step 2:
Now find the inverse of the cosine to obtain the value of [tex]x[/tex] as,
[tex]\begin{gathered}x={\cos^{-1}}\left({0.34}\right)\hfill\\x=70.12^\circ\hfill\\\end{gathered}[/tex]
Step 3:
Now round the value of [tex]x[/tex] to the nearest whole degree.
[tex]x=70^\circ[/tex]
Therefore, the value of [tex]\angle BAC=x=70^\circ[/tex] .
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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
