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From point A, a perpendicular AC and a slope AB are drawn to plane a A.D. Find the length of the slope AB, IF
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Answer to a math question From point A, a perpendicular AC and a slope AB are drawn to plane a A.D. Find the length of the slope AB, IF
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рішення:
За теоремою Піфагора,
AD^2=AC^2+CD^2
AC^2=AD^2-CD^2
AC=\sqrt{AD^2-CD^2}
AC=\sqrt{20^2-12^2}
AC=\sqrt{400-144}
AC=\sqrt{256}
AC=16см
За тригонометрією прямокутного трикутника,
\sin\theta=\frac{проти {гіпотенузи}
\sin\кут ABC=\frac{AC}{AB}
AB=\frac{AC}{\sin\angle ABC}
AB=\frac{16}{\sin45^{\circ}}
AB=16\sqrt{2}см
Відповідь: AB=16\sqrt{2}см
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