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Triangle Trigonometry Worksheet

Triangle Trigonometry Worksheet
  • Page 1
 1.  
In the figure, if R = 90°, P = 35°25′, QSR = 62°30′ and RS = 18.3, then what is the length of PQ?

a.
43.1
b.
49.4
c.
25
d.
60.7


Solution:

tan 62°30′ = QR18.3
[tan S = QR / SR.]

QR = 18.3 tan 62°30′

QR = 18.3 × (1.920982127)

QR = 35.15

sin 35°25′ = 35.15PQ
[sin P = QR / PQ.]

PQ = 35.15 sin 35°25'

PQ = 60.7
[Simplify using calculator.]


Correct answer : (4)
 2.  
In the figure, if C = 90°, A = 34°20′, DC = 8.4 and BC = 20.5, then the measure of ABD is:

a.
55°36′
b.
67°44′
c.
22°16′
d.
33°24′


Solution:

tan DBC = 8.420.5
[tan DBC = DC / BC.]

tan DBC = 0.409756097

DBC = 22°16′

ABD = 180° – (34°20′ + 90° + 22°16′)

= 180° - 146°36′ = 33°24′


Correct answer : (4)
 3.  
The measure of one acute angle of a right triangle is 78°. Find the other acute angle in the triangle.
a.
102°
b.
12°
c.
78°
d.
22°


Solution:

The sum of the measures of the two acute angles of a right triangle is 90°.

If one acute angle of a right triangle is 78°, then the measure of the other acute angle is 90° - 78° = 12°.


Correct answer : (2)
 4.  
The measure of one acute angle of a right triangle is 32° 43′. The other acute angle of the triangle is:
a.
58°17′
b.
57°27′
c.
58°43′
d.
57°17′


Solution:

The sum of the measures of the two acute angles of a right triangle is 90°.

If one acute angle of a right triangle is 32° 43′, then the measure of the other acute angle is: 90° - 32° 43′ = 89° 60′ - 32° 43′ = 57° 17′.


Correct answer : (4)
 5.  
The angle of elevation of the top of a pole measures 48° from a point on the ground 18 ft from the base of it. Fnd the height of the flagpole.
a.
22 ft
b.
12 ft
c.
18 ft
d.
20 ft


Solution:


Let x be the height of the flagpole.

tan 48° = x18

x = 18 tan 48°

x = 18 × (1.110612515) = 20

So, the height of the flagpole is 20 ft.


Correct answer : (4)
 6.  
A pillar of height 200 ft casts a shadow of 320 ft long. Find the measure of the angle of elevation of the sun.
a.
51°19′
b.
32°
c.
58°
d.
38°40′


Solution:


Let AB = 200 ft be the length of the pillar.

Let BC = 320 ft be the length of the shadow.

ACB is the angle of elevation of the sun.

tan C = 200320
[tan C = AB / BC.]

tan C = 0.625

C = 32°


Correct answer : (2)
 7.  
In right triangle PQR, if Q = 90°, R = 22° and q = 35, then the measure of r to two significant digits is ____.


a.
15
b.
32
c.
13
d.
35


Solution:

sin 22° = r35
[sin R = rq.]

r = 35 × sin 22° = 35 × (0.374606593)

= 13, to two significant digits


Correct answer : (3)
 8.  
In right triangle ABC, if B = 90°, C = 70° and c = 18, then the measure of b to two significant digits is:


a.
18
b.
16
c.
19
d.
29


Solution:

sin 70° = 18b
[sin C = cb.]

b = 18sin 70°

b = 18 csc 70°

= 18 (1.064177772) = 19, to two significant digits


Correct answer : (3)
 9.  
In right triangle DEF, if D = 42°, E = 90° and f = 32, then the measure of e to two significant digits is:


a.
24
b.
29
c.
43
d.
21


Solution:

cos 42° = 32e
[cos D = fe.]

e = 32cos 42°

e = 32 sec 42°

= 32 × 1.34563273 = 43, to two significant digits


Correct answer : (3)
 10.  
In right triangle PQR if Q = 90°, R = 30° and r = 12, then the measure of p to two significant digits is:


a.
21
b.
11
c.
12
d.
24


Solution:

cot 30° = p12
[cot R = pr.]

p = 12 cot 30°

p = 12 × 1.732050808 = 21, to two significant digits.


Correct answer : (1)

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