3.1.1. The line y = x intersects the unit circle at two points. What are

Homework Assignment
Solutions
Section 3.1
1
2x
3.1.1. The line y =
intersects the unit circle at two points.
What are they? Round to two decimal places.
6
a
Answer: (0.89, 0.45) and (−0.89, −0.45)
3.1.2. The line y = − 12 x intersects the unit circle in two
places. What are they? Round to two decimal places.
Answer: (0.89, −0.45) and (−0.89, 0.45)
3.1.3. The function f (x) = 2|x| intersects the unit circle in
two places. What are they? Round to two decimal
places.
Answer: (−0.45, 0.89) and (0.45, 0.89)
5
Answer: 3.32
3.1.11. What is the linear distance between the points (−3, 1)
and (2, −4) in the xy-plane? That is, what is the length
of the line in the image shown below? Leave your answer in exact form. Hint: Try drawing a right triangle
with the line whose length you want as the hypotenuse.
y
3.1.4. A right triangle has legs with lengths 4 in and 6 in.
What is its area?
Answer: 12 in2
1
x
-4
-3
-2
-1
1
2
3
4
-1
3.1.5. A right triangle has a hypotenuse of length 10 cm. If
one of its legs is twice as long as the other, find its
perimeter. Leave your answer in exact form.
√
Answer: 10 + 6 5 cm
3.1.6. Angles θ and φ are supplementary. If φ is 10◦ larger
than θ, find both angles.
Answer: θ = 85◦ and φ = 95◦
3.1.7. Mark goes jogging one morning. He leaves his house
and jogs 3 mi north and he then turns right and jogs
5 mi east before he stops to stretch. At that point,
how far away from his house is he (in a straight line)?
Round your answer to two decimal places.
Answer: 5.83 mi
3.1.8. Dale and Betty go through a traffic light at the same
time but Dale goes straight and Betty turns right. After two minutes Dale is 2000 yd from the intersection
and Betty is 750 yd from the intersection. Assuming
the roads met at a right angle and both were perfectly
straight, how far are Dale and Betty away from each
other after two minutes? Round your answer to two
decimal places.
Answer: 2136.00 yd
-4
√
Answer: 5 2
3.1.12. A television set has a rectangular screen (assume that
the corners are not rounded). If it is 48 in wide and
27 in tall, how far does the screen measure from corner
to corner? Round your answer to two decimal places.
Answer: 55.07 in
3.1.13. Consider a right triangle whose hypotenuse has a
length of 53 in. If one leg is 17 in longer than the other
leg, find the perimeter of the triangle. Round your
answer to two decimal places.
Answer: 126 in
3.1.14. The hypotenuse of a right triangle has a length of 200
and the longer leg is three times as long as the shorter
leg. Find the perimeter of the triangle. Round to two
decimal places.
Answer: 452.98
Answer: 24.08 in2
80◦
θ
Answer: 160◦
3.1.10. Find the value of a below. Round your answer to two
decimal places.
Last Updated: April 21, 2014
-3
3.1.15. A pizza box is rectangular. If it is 16 in wide and 18 in
tall, how far does the box measure from corner to corner? Round your answer to two decimal places.
3.1.9. Find the angle θ below.
80◦
-2
3.1.16. A particular township is in the shape of a rectangle
which is 4 mi on one side and 6 mi on the other side.
A hiker wants to hike the longest possible distance in
a straight line without leaving the township so she decides to hike from the northeast corner to the southwest corner. How far is her hike? Round to two decimal places.
Answer: 7.21 mi
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