SOLUTION: Please help me solve this, its for a quiz grade and im clueless on how to solve this.
Show that in a 30-60-90 triangle, the altitude to the hypotenuse divides the hypotenuse in th
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-> SOLUTION: Please help me solve this, its for a quiz grade and im clueless on how to solve this.
Show that in a 30-60-90 triangle, the altitude to the hypotenuse divides the hypotenuse in th
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Question 577147: Please help me solve this, its for a quiz grade and im clueless on how to solve this.
Show that in a 30-60-90 triangle, the altitude to the hypotenuse divides the hypotenuse in the ratio 1:3. In triangle ABC let CD be the altitude to the hypotenuse and DB=x Answer by solver91311(24713) (Show Source):
Presume vertex A is the 60 degree angle, then in triangle ACD, angle A is 60 degrees and angle ADC is 90 degrees, so angle ACD must be 30 degrees, therefore triangle ACD is similar to triangle ABC (by Angle-Angle-Angle). Similarly you can show that triangle BCD is also similar to ABC.
Since in a 30-60-90 right triangle the short leg is one-half of the hypotenuse, AC must be one half of AB and furthermore AD is one half of AC hence AD is one-fourth of AB. Therefore the ratio of AD to DB is 1/4 to 3/4 which is equivalent to 1:3.
John
My calculator said it, I believe it, that settles it
