The value hypotenuse of given triangle is [tex]\fbox{\bf 6 units}[/tex].
Further explanation:
Method 1:
Pythagoras theorem:
For a [tex]\triangle ABC[/tex], right angle at [tex]B[/tex] following relation holds:
[tex]{\left({AC}\right)^2}={\left( {AB}\right)^2}+{\left( {BC}\right)^2}[/tex] ……(1)
Consider the given triangle as [tex]\triangle ABC[/tex] shown below in Figure 1.
Substitute [tex]3\sqrt 2[/tex] for [tex]AB[/tex], [tex]3\sqrt 2[/tex] for [tex]BC[/tex] and [tex]h[/tex] for [tex]AC[/tex] in equation (1).
[tex]\begin{aligned}{h^2}&={\left( {3\sqrt2}\right)^2}+{\left({3\sqrt2}\right)^2}\\{h^2}&=18+18\\{h^2}&=36\\h&=6\\\end{aligned}[/tex]
Thus, the value hypotenuse of given triangle is [tex]\fbox{\bf 6 units}[/tex].
Method 2:
Consider the given triangle as [tex]\triangle ABC[/tex] as shown below in Figure 1.
In right [tex]\triangle ABC[/tex], [tex]BC[/tex] is base, [tex]AB[/tex] is perpendicular and [tex]AC[/tex] is hypotenuse.
[tex]sin[/tex] is defined as the ratio of perpendicular to hypotenuse, [tex]cos[/tex] is defined as the ratio of base to hypotenuse and [tex]tan[/tex] is defined as the ratio of perpendicular to base. There exists three more ratios which are reciprocal of [tex]sin,cos[/tex] and [tex]tan[/tex].
For [tex]\angle C[/tex], these ratios can be listed as shown below.
[tex]\begin{aligned}{\text{sinC=}}\frac{{AB}}{{AC}},\,{\text{\,\,\,\,\,\,\,\,cosecC=}}\frac{{AC}}{{AB}}\hfill\\{\text{cosC=}}\frac{{BC}}{{AC}},{\text{\,\,\,\,\,\,\,secC=}}\frac{{AC}}{{BC}}\hfill\\\tan C {\text{}}\frac{{AB}}{{BC}},\,\,\,\,\,\,\,\,\,\,\cot\,C{\text{=}}\frac{{BC}}{{AB}} \hfill\\\end{aligned}[/tex]
Substitute [tex]3\sqrt 2[/tex] for [tex]AB[/tex], [tex]h[/tex] for [tex]AC[/tex] and 45 for [tex]\angle C[/tex].
[tex]\begin{aligned}{\text{sin45=}}&\frac{{3\sqrt2}}{h}\hfill\\\frac{1}{{\sqrt2}}&=\frac{{3\sqrt 2 }}{h}\hfill\\h&=\left({3\sqrt2}\right)\left({\sqrt2}\right)\hfill\\h&=6\hfill\\\end{aligned}[/tex]
Thus, the value hypotenuse of given triangle is [tex]\fbox{\bf 6 units}[/tex].
Learn more:
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Answer Details :
Grade: Senior School
Subject: Mathematics
Chapter: Triangle.
Keywords:
triangle ABC, sin, cos, tan, cot, sec, cosec, angle, Pythagoras theorem, hypotenuse, base, perpendicular, trigonometric ratio, similarity, ratio of sides, right triangle, similar triangle, ratio of sides, equal angles, square of hypotenuse, sum, square of legs, sum of square of legs, sum of angle of triangle, property of triangle, triangle ABC.
