Download p1 mod 2 review sheet aims 16-29

Review Sheet Aims 16-29
CC Geometry H
1) Find the unknown variables. All answers must be in simplest radicalform:
c)
a)
b)
d)
e)
2) Using the following diagram, find AB, AC, DC, DB.
3) Find the exact value of the length of the altitude of an equilateral
triangle whose sides measure 12 inches.
4) In isosceles ΔABC, vertex ≮C measures 120º and the length of AC is 8.
a) Find the length of the altitude drawn from C
b) Find the exact length of AB.
5) The diagonal of a square measures 3√2. Find the perimeter of the square.
6) The ratio of the measure of the angles of a triangle is 1:2:3. The length
of the shortest side is 8. What is the exact length of the perimeter of
the triangle? 7a) Given the diagram of the triangle, complete the table,
with all entries in simplest radical form.
b) Draw and label the sides and angles of a right triangle using the above ratios.
By what criterion is the new triangle similar to the original?
8) The sine of an angle is equal to the __________ of its _________________.
9) Find the value of the missing variables in simplest radical form, if necessary.
10) Find ML, JL, JK, and KL in simplest radical form, if necessary.
11) The sides of a right triangle are 5, 12, and 13. Find the length of the altitude
drawn to the hypotenuse in simplest radical form, if necessary.
12) For the given obtuse triangle, calculate the missing side length to the nearest
tenth.
4
100o
25o
7.3
13) For the diagram to the right:
a) Find the measure of angle A.
b) Find the height of the building to the nearest foot.
c) Find the length of the indicated ray of sunlight to
the nearest foot.
80 ft
14) Jen's cat is stuck in her backyard tree. A fireman positions a ladder against
the tree and rescues the cat. The ladder was extended to 22 ft and made an angle
of 62 degrees with the ground. What was the cat's vertical height, to the nearest
tenth of a foot?
15) Given right triangle GHI below, find the measures of the remaining angle and
G
sides (to the nearest tenth).
8.4
61
H
I
16) Find x to the nearest hundredth.
a)
17) If sin θ =
b)
, use trigonometric identities to find cos θ and tan θ.
18) If tan θ = 2/5, use the Pythagorean theorem to find the hypotenuse, and
then find cos θ and sin θ.
19) In the diagram of the right square pyramid below, the sides of the base are 5.8
units. Find the height of the pyramid to the nearest tenth.
68o
20) Find x to the nearest tenth of a degree:
a)
b)
c)
21) A ship is at position A on the sea surface and locates a wreck, C, on the seabed
321 m vertically below. The ship then steams 525 m due west until it reaches
position B. From its new position at B,
525 m
what is the size of the angle of
depression from B to the wreck C, to
the nearest degree?
321 m
22) Find the length of side p and the measure of angle m, as shown in the diagram.
Give each answer correct to the nearest whole number or degree.
23) Ray has a rolling backpack that is 3.75 feet tall when the handle is extended.
His hand is 3 ft from the floor when he is pulling the backpack. What angle does
his backpack make with the floor? Round to the nearest degree.
24) Round answers to the nearest tenth.
a) Find the length of the hypotenuse.
15
b) Find the length of the longer leg.
8
270
370
25) Find the perimeter and area, in simplest radical form, of a right triangle with
sides 3√300, 10√48 and 25√12.
26) Complete the chart with exact values:
θ
300
00
450
900
600
sin θ
cos θ
Using the exact values:
a) Express in simplest form the sum: sin 30 + cos 60
b) Express in simplest form the sum: sin 45 + cos 45
c) Express in simplest form the sum: 2sin 60 - cos 30
d) Find the value of θ that makes each statement true.
(1) sin θ = cos(3θ - 10)
(2) cos (45 - θ) = sin 4θ
27) Find the unknown lengths, using sin and cos values of an acute angle.
a)
45
b
b)
0
b
5√2
c)
300
6√3
600
a
a
15
a
b
28) A person standing at point P looks up to the top of a flagpole,
0
with angle of elevation 57 . Find, to the nearest foot,
the distance from point P to the top of the flagpole if the
flagpole is 48.7 feet tall.
P
29) Ted is estimating the height of the Space Needle
0
using the angle of elevation of 75 from his eye level
to the top of the Needle. If Ted's level is 5.75 ft above
the ground, and the distance from Ted to the
Space Needle is 50 ft., how tall is the Space Needle?
(nearest foot)
0
30) A line on the coordinate plane makes an angle of depression of 76 with a
horizontal line. Find the slope of the line, to the nearest ten-thousandth.
0
31) Find, to the nearest tenth, the area of ΔRST if RS = 9, RT = 14 and m≮R = 64 .
32) In ΔLTV, TV = 20, LT = 15.6, m≮L = 88, m≮V = 50, find the area of ΔLTV,
to the nearest tenth.
0
33) A triangle has two sides of length 4, with an angle of 51 between them.
What is the length of the remaining side and the area of the triangle, to the
nearest tenth?