# Length and Angles of Triangles, Interest, and Total Payment

1. If the hypotenuse of a right triangle is 1m more than the longer leg, and the shorter leg is 9m long, find the length of the longer leg. The longer led is_____m.

2. Find the finance charge on an unpaid balance of $1818.86 in a revolving charge account if the monthly interest rate is 1.7%. The finance charge is $______(round to the nearest cent).

3. In triable ABC, angles A and B have the same measure, while the measure of angle C is 57 degrees less than the measure of either. What are the measures of the three angles? Angles A and B measure_____degrees each. Angle C measures____degrees.

4. Find the present value of the following future amount, $600,000, at 10% compounded annually for 25 years. What is the present value?

5. Suppose the $250,000 is owed on a house after the down payment is made. The monthly payment for principal and interest at 9.0% for 30 years is 250*8.04623=$2,011.56. What is the total amount that will be paid for principal and interest? If the total interest charged is the total amount paid minus the amount financed, what is the total interest?

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#### Solution Preview

1. Let L = the length of the longer leg, S = the length of the shorter leg, H = the length of the hypotenuse of the right triangle.

By Pythagorean theorem, L^2+ S^2= H^2. Since H is 1m 'longer' than the longer leg, L, H = L + 1. Also, the length of the shorter leg is given as 9m.

Therefore, L^2+9^2= 〖(L+1)〗^2= L^2+2L+1 (expand the factor, (〖L+1)〗^2)

Subtract L^2 and 1 from both sides and you will get:

80 = ...

#### Solution Summary

This solution provides calculations for finding the length of a triangle, angle of a triangle, interest and total payment.