SOLUTION: The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments whose lengths are in the ratio 3:2. The length of the altitude is 18 feet. Find: a.)the le

Question 110076: The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments whose lengths are in the ratio 3:2. The length of the altitude is 18 feet.
Find:
a.)the length of the hypotenuse in simplest radical form.
b.)the length of the hypotenuse to the nearest inch.
c.)the length of each leg of the triangle in simplest radical form.
d.)the length of each leg of the triangle to the nearest inch.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
The hypotenuse is the base of the triangle.
the altitude divides the 90 deg angle 3:2 also 54:36 deg.
tan(36)=x/18
x=18tan(36)=13.0778'
x=18tan(54)=24.7749'
hyp=13.0778+24.7749=37.8526'=37'10"
short side: 18^2+13.0778^2=495.028
sqrt(495.028)=22.2492'=22'3"
long side: 18^2+24.7749^2=937.794
sqrt(937.794)=30.6234'=30'7"
Check:
22.2492^2+30.6234^2=1432.82
sqrt(1432.82)=37.8526' hyp
Ed
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