Trigonometric Ratios Worksheet

Trigonometric Ratios Worksheet
  • Page 1
 1.  
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 flag pole.
a.
18 ft
b.
12 ft
c.
20 ft
d.
22 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 flag pole is 20 ft.


Correct answer : (3)
 2.  
In right triangle PQR, if Q = 90°, R = 22° and q = 35, then the measure of r to two significant digits is ____.


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


Solution:

sin 22° = r35
[sin R = rq.]

r = 35 × sin 22° = 35 × (0.374606593)

= 13, to two significant digits.


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

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


Solution:

Sin 70° = 18b
[sin C = cb.]

b = 18sin70o

b = 18 csc 70°

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


Correct answer : (2)
 4.  
In right triangle DEF if D = 42°, E = 90° and f = 32, then the measure of e to two significant digits is:


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


Solution:

cos 42° = 32e
[cos D = fe.]

e = 32cos 42°

e = 32 sec 42°

= 32 × 1.34563273 = 43, to two significant digits.


Correct answer : (1)
 5.  
In right triangle PQR if Q = 90°, R = 30° and r = 12, then the measure of p to two significant digits is:


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


Solution:

cot 30° = p12
[cot R = pr.]

p = 12 cot 30°

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


Correct answer : (2)
 6.  
In an isosceles triangle ABC, if b = 18, c = 18 and C = 50°, then the length (to two significant digits) of side a is:


a.
43
b.
27
c.
23
d.
30


Solution:

The altitude from A to BC divides the triangle into two congruent right triangles.

In right triangle ADC, DC = 12(a).

Cos 50° = a218 = a36
[cos C = DC / AC.]

a = 36 Cos 50° = 36(0.642787609) = 23, to two significant digits.


Correct answer : (3)
 7.  
In an isosceles triangle ABC, if b = 20, c = 20 and C = 70°, then the length (to two significant digits) of the altitude drawn from A to BC is:

a.
18
b.
15
c.
19
d.
23


Solution:

The altitude from A to BC divides the triangle into two congruent right triangles.

In right triangle ADC, sin C = AD / AC

sin 70° = AD20

AD = 20 × sin 70° = 20 × (0.93969262)

AD = 19, to two significant digits.


Correct answer : (3)
 8.  
In right triangle ABC if C = 90°, B = 28°20′, and b = 11.8, then the length of c to three significant digits is:
a.
11.8
b.
20.7
c.
24.9
d.
13.4


Solution:


sin 28°20′ = bc
[sin B = AC / AB.]

sin 28°20′ = 11.8c

c = 11.8sin28o20'

c = 24.86302319 = 24.9, to three significant digits.


Correct answer : (3)
 9.  
Find the value of sin A, if x = 5 units, y = 12 units and a = 13 units.

a.
12 13
b.
13 12
c.
5 13
d.
13 5


Answer: (c)


Correct answer : (3)
 10.  
D is a point on side BC of ΔABC such that mADC = mBAC. If CA = 10 cm. and CB = 15 cm, then what is the length of CD?
a.
6.66 cm
b.
22.5 cm
c.
5 cm
d.
7.5 cm


Answer: (a)


Correct answer : (1)

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