In ΔCDE, the measure of ∠E=90°, the measure of ∠C=16°, and EC = 65 feet. Find the length of DE to the nearest tenth of a foot.

Given:

Given that the triangle CDE is a right triangle.

The measure of ∠E is 90° and the measure of ∠C is 16° and the length of EC is 65 feet.

We need to determine the length of DE.

Length of DE:

The length of DE can be determined using the trigonometric ratio.

Thus, we have;

where the angle is 16° and the side opposite to the angle is DE and the side adjacent to the angle is EC.

Substituting the sides, we get;

Substituting DE = 65, we have;

Multiplying both sides by 65, we have;

Thus, the length of DE is 18.6 feet.

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step-by-step explanation:

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.