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Name:
Date:
Math 2
Trigonometry Quiz Review
1. Find x and y using trigonometry.
20°
2. Find the missing information to the nearest hundredth.
a. Find length w
b. Find mX
19º
17
19º17
w
17
X
5
17
5
w
X
3. Finds the missing parts of this triangle by creating two right triangles.
mQ = ____________
mP = _____________
side length p = ________
Name:
Date:
Math 2
4. Grand Canyon Problem From a point on the North
Rim of the Grand Canyon, a surveyor measures an angle
of depression of 1.3 to a point on the South Rim. From
an aerial photograph, he determines that the horizontal
distance between the two points is 10 miles. How many
feet is the South Rim below the North Rim.
5. Find x and y
x
5
30°
y
6. This right triangle has an area of 50. Find it's height and the measure of angle x.
7. Find x and then y. (Hint: the parallel lines are important!)
5
9
yº
x
x+3
Name:
Date:
Math 2
8. Each of the right triangles below is an isosceles right triangle. Find the lengths of
̅̅̅̅̅
̅̅̅̅̅.
𝑆𝑊 , ̅̅̅̅̅
𝑇𝑊 , ̅̅̅̅̅
𝑈𝑊 , and 𝑉𝑊
9. Find the perimeter and area of ACDB. Note that the area of a trapezoid = ½(b1+b2)h.
Area = ______________________
Perimeter = ___________
10. Missile Problem An observer 5.2 km from the launch pad observes a missile ascending.
a. At a particular time, the angle of elevation is 31.45. How high is the
missile? How far is it from the observer?
b. What will the angle of elevation be when the missile reaches 30 km?
11. Airplane Landing Problem Commercial airliners fly at an altitude of about 10 km. They
start descending toward the airport when they are far away, so that they will not have to dive at
a steep angle.
a. If the pilot wants the plane’s path to make an angle of 3 with the ground, at what
horizontal distance from the airport must she start descending
b. If she starts descending a ground distance of 300 km from the airport, what angle will
the plane’s path make with the horizontal?
12. Radiotherapy Problem A beam of gamma rays is to be used
to treat a tumor known to be 5.7 cm beneath the patient’s
skin. To avoid damaging a vital organ, the radiologist moves
the source over 8.3 cm.
a. At what angle to the patient’s skin must the radiologist aim
the gamma ray source to hit the tumor?
b. How far will the beam have to travel through the patient’s body before reaching the tumor?
Name:
Date:
Math 2
Answer Key
1. x =
4
= 11.695
sin(20°)
2. a. w =
y=
5
= 14.619
sin(20°)
æ5ö
17
= 17.98 b. mÐX = sin -1ç ÷ = 17.105°
è17 ø
cos(19°)
3. h = altitude drawn from vertex P = 6.5sin(27.3) = 2.98
æ h ö
mP = 134.003
p = 9.3cos(Q) + 6.5cos(27.3) =
mÐQ = sin -1ç ÷ = 18.697°
è 9.3 ø
14.585
4. h = 1198.2 ft
5√6
5. x = 5√2
y=
6. h = 20
æhö
x = tan -1ç ÷ = 75.964°
è5ø
7.
2
5
x
=
so x = 3.75
14 2x + 3
æ10.5 ö
y = sin-1ç
÷ = 48.59°
è 14 ø
̅̅̅̅̅ = 4.
8. ̅̅̅̅̅
𝑆𝑊 = √2, ̅̅̅̅̅
𝑇𝑊 = 2, ̅̅̅̅̅
𝑈𝑊 = 2√2, 𝑉𝑊
9. Height of the trapezoid is 6 3 so the length of the second base is 14 + 6 3 . The
length of the last side is 6 6 . The area is
A = 12 8 +14 + 6 3 6 3 = 66 3 + 54 =168.315. The perimeter P = 6 6 + 8 +
(
)( )
12 + 14 + 6 3 = 59.089.
10. a) 3.18 km high, 6.095 km away b) 80.166
11. a) d = 190.811 km b) 1.909
12. a) 34.479 b) 10.069 cm