Agarden in the shape of a right triangle has sides measuring 60, 80 and 100 ft. the owner of the garden adds a new section of fence that runs from the right angle to the hypoteneuse and separates the garden into two parts of equal perimeter. find the length of the new section of the fence. problem is not out of a textbook, rather on a worksheet.

The answer is 48 ft

Step-by-step explanation:

Step 1:

The garden before the fence is: (refer to graphical representation in attached file)

o = side

b = base

h= hypotenuse  

Use Sin (t) formula;

Sin (t) = o/h

Sin (t) = 80/100

Sin (t) = 0.8

Step 2:

The garden was divided in 2 parts and a is the missing length which needed to be found (refer to graphical representation in attached file)

For Small triangle (refer to graphical representation in attached file);

a = side

c = base

b= hypotenuse  

Use Sin (t) formula;

Sin (t) = a/b

0.8 = a/60

A = 0.8x60

A = 48 ft

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.