In a right-angled triangle abc, the height bc is drawn, find the length of the hypotenuse ac
| September 1, 2021 | education
In a right-angled triangle abc, the height bc is drawn, find the length of the hypotenuse ac, if the angle abc = 60 degrees, cd = 2 cm
Determine the value of the angle CBD. Angle CBD = ABC – ABD = 90 – 60 = 30.
Since BD is the height of the ABC triangle, then the BCD triangle is rectangular, in which the CD leg lies opposite the angle 30, then BC = 2 * CD = 2 * 2 = 4 cm.
The ABD triangle is also rectangular, then the angle BAD = (180 – 90 – 60) = 30.
The BC leg of the ABC triangle lies opposite the angle 30, then AC = 2 * BC = 2 * 4 = 8 cm.
Answer: The length of the AC hypotenuse is 8 cm.
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