Homework Assignment
Solutions
3.5.1. Compute the following and leave your answers in exact
form:
(a) tan(30◦ )
(b)
(c)
(d)
(e)
(f)
Section 3.5
Answer: 117.95
3.5.6. Find ` below. Round to two decimal places.
√
Answer: 33
tan(45◦ )
Answer: 1
tan(60◦ )
√
Answer: 3
tan(135◦ )
Answer: −1
tan(225◦ )
Answer: 1
tan(−60◦ )
√
Answer: − 3
38◦
21
`
Answer: 16.41
3.5.7. Find y in the following diagram. Round your answer
to two decimal places.
3.5.2. Find tan(θ) in the triangle below and leave your answer
in exact form.
50
16
20
θ
y
Answer:
√8
561
3.5.3. Find tan(θ) in the triangle below and leave your answer
in exact form.
50◦
Answer: 13.11
25
7
θ
Answer:
38◦
3.5.8. Find an equation for the line graphed below and leave
your answer in exact form. (Assume that the line goes
through the point (1, 0) as it appears.)
7
24
y
3.5.4. Find the value of a below. Round your answer to two
decimal places.
6
5
4
a
62◦
3
2
1
5
60◦
x
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
-1
Answer: 2.66
-2
3.5.5. Find ` below and round to two decimal places.
-3
-4
42◦
-5
-6
131
Answer: y =
√
3x −
√
3
`
Last Updated: March 29, 2014
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Homework Assignment
Solutions
3.5.9. The function f (x) is a linear function. It has an xintercept of (−3, 0) and it intersects the x-axis at an
angle of 60◦ . Find the y-intercept of f and leave your
answer in exact form.
√
Answer: (0, 3 3)
3.5.10. The function f is linear, f (1) = −4, and f intersects
the x-axis at an angle of 150◦ (measured counterclockwise from the x-axis, as usual). Find a formula for f
and leave your answer in exact form.
3
3 x
3.5.13. The area of the outermost triangle shown below is 5 in2 .
Find the perimeter of the large triangle and round your
answer to two decimal places. Remember: The perimeter of a shape is the distance around the outside of it.
30◦
√
√
Answer: f (x) = −
Section 3.5
−4+
3
3
3.5.11. The top of a 200 ft vertical tower is to be anchored
by cables that make an angle of 60◦ with the ground.
Round your answers to two decimal places.
(a) How long must the cables be?
Answer: 230.94 ft
(b) How far from the base of the tower should anchors
be placed?
Answer: 115.47 ft
3.5.12. The front door to the student union is 20 ft above the
ground and it is reached by a flight of steps. The school
wants to build a wheelchair ramp with an incline of 15◦
from the ground to the door. How much horizontal distance is needed for the ramp? Round to two decimal
places.
5 in
Answer: 11.52 in
3.5.14. A ramp is to be built that has a 12◦ angle of incline
which climbs a total of 4 ft. How long does the base
of the ramp need to be? Round your answer to two
decimal places.
Answer: 18.82 ft
3.5.15. An airplane takes off at an angle of 8◦ from a runway. If there are 2000 ft of runway remaining when the
airplane lifts off, find the airplane’s height above the
ground when it passes the end of the runway. Round
to two decimal places.
Answer: 281.08 ft
Answer: 74.64 ft
Last Updated: March 29, 2014
Page 2 of 2