1. An Application of Trigonometry Heights and Distances

2. Solution: y x 10 miles C P Station A Station B
Problem 1. A pilot sends out a distress call. Her altimeter and GPS are malfunctioning. She is able to maintain her heading and speed, but doesn’t know her elevation or exact location. She is directly between two radar stations, Station A and Station B, which are 10 miles apart. The angle of elevation to one radar station is 15o and the angle of elevation to the second is 10o.
What is her elevation and what is her horizontal distance from each station?
Solution: C y
150
100 x P
10 - x
Station A
Station B
10 miles

3. y y 10-x x (10−𝑥) (10−𝑥) .𝑥 𝑥. C C 𝑡𝑎𝑛𝜃= 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 B P A P
Compute: 𝑥, 10−𝑥 , 𝑎𝑛𝑑 𝑦.
Recall: In a right triangle,
𝑡𝑎𝑛𝜃= 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝜃
Opposite
Adjacent
Hypotenuse
150 x A P y C
10-x
100 C y B P
(10−𝑥)
(10−𝑥) 𝑥. .𝑥
Writing these equations in a matrix form as :

4. Conclusion: The elevation of the pilot is 1.06 miles and
her horizontal distance from the station A and
the station B is 3.97 miles and miles respectively.

5. ApPendix Solving System of Linear Equation using TI-89
Consider two linear equations
Matrix method
1)Go to the math menu by pressing 2nd, MATH.
2)Then go into Matrix and select the rref( Function.
3)Then type the matrix as shown below and press enter.
4)The last column is the solution.

6. Finance Annuity

7. Recall (Ordinary annuity):
Problem 2. Anne purchases a house for $175,000 and puts 20% down. She finances the rest with a 30 years mortgage at 4% interest.
What are her monthly payments for principal and interest?
If she sells the house in 10 years, what will the remaining balance on her mortgage be?
Recall (Ordinary annuity):
PV = Present value
FV = Future value
t = Time in years
r = Annual rate of interest
m = Regular Periodic payment
n = # payments made per year

8. Given:
To compute:
Down payment=
Amount to finance =
Now, we find the monthly mortgage payment(m) for $140,000 at 4% for 30 years.

9. We have,
PV = $140,000
r = 4%=0.04
t = 30 years
n = 12
The monthly payment for the mortgage is $668.38

10. 2. what is the remaining balance of the mortgage in 10 years?
Remaining balance = Future value of the loan - Future value of the annuity
We have,
PV = $140,000
m = $668.38
r = 4%=0.04
t = 10 years
n = 12
Conclusion: Anne’s monthly payment for the mortgage is $ and her remaining balance of the mortgage in 10 years is $110,
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