Chapter 10 - NCPN

3 Cale, Tammie, and Allison are members of the ultimate flying disc team. The
object of the game is to score points by receiving a teammate’s pass of the flying
disc in the opposing team’s end zone. Players may not run when in possession
of the disc. Cale had the disc and passed it to Tammie, who was 18 meters
away. Tammie then passed the disc to Allison in the end zone 28 meters away.
When viewing the instant replay, the statistician calculated the measured angle
formed by the straight line going from Cale to Tammie and the straight line
going from Tammie to Allison to be 75°. Use the facts that sine and cosine of 45°
is 1 2 , the sine of 30° is 1 2 , and the cosine of 30° is 3 to find cosine 75°.
2
a. If the straight line distance from Cale and Allison is a and the measure of
the angle formed by the straight line going from Cale to Tammie and the
straight line going from Tammie to Allison is A, use the Law of Cosines to
write a 2 in terms of cos A. a 2 = 1,108 – 1,008cos A
b. The angle formed by the straight line going from Cale to Tammie and the
straight line going from Tammie to Allison measured 75°. What angle sum
identity can the statistician use to solve for a in the equation given in the
answer to part a cos (A + B) = cos A cos B – sin A sin B
c. Substitute the values the statistician knows into the angle sum identity
given in the answer to part b. cos (30° + 45°) =
3 1 1 1
• − •
d. Simplify the answer given to part c to solve for the cosine of 75° to the
nearest hundredth. 0.26
e. Substitute the answer given in part d for cos A in the answer given in part a
and solve for a, which is the straight-line distance from Cale to Allison.
Round to the nearest tenth. 29.1 m
2
2
2
2
Agriculture &
Agribusiness
4 A combine is a machine that picks, thrashes, and cleans grain
while traversing a field. Avery has a reclining backrest on her
combine to increase comfort. The measure of the angle formed
by the combine’s seat and the reclining backrest can range from
90° to 135°. The equation tan 2 θ – 6tan θ – 16 = 0 represents
this situation where θ is the measure of the angle formed by the
combine’s seat and the reclining backrest. Avery wants to solve for
θ so she can adjust her reclining backrest to this angle in the future.
a. What type of trigonometric equation does Avery have to solve
to find θ quadratic
b. When tan θ is substituted for x, four possible angle measures emerge.
Explain why three of them can not be correct. see margin
c. What is the measure of the angle formed by the reclining backrest and the
seat Round to the nearest tenth degree. 116.6°
Math Applications 497