EduSahara™ Assignment
Name : Trigonometry Diagram Problems
Chapter : Introduction to Trigonometry
Grade : CBSE Grade X
License : Non Commercial Use
Question
1
1.
In the given figure, △IJK is right angled at J. If JK = 8 cm and ∠K = 30°, find IJ and IK
(i)
8
3
4
√
3
cm
&
16
cm
(ii)
8
3
4
√
3
cm
&
18
cm
(iii)
8
3
cm
&
18
cm
(iv)
8
3
√
3
cm
&
16
3
√
3
cm
(v)
8
3
4
√
3
cm
&
16
3
√
3
cm
Question
2
2.
In the given figure, △EFG is right angled at F. If FG = 12 cm and ∠G = 45°, find EF and EG
(i)
11
cm
&
27
cm
(ii)
13
cm
&
24
cm
(iii)
13
cm
&
12
√
2
cm
(iv)
13
cm
&
27
cm
(v)
12
cm
&
12
√
2
cm
Question
3
3.
In the given figure, △DEF is right angled at E. If EF = 9 cm and ∠F = 60°, find DE and DF
(i)
9
cm
&
19
cm
(ii)
9
√
3
cm
&
18
cm
(iii)
9
4
√
3
cm
&
19
cm
(iv)
9
4
√
3
cm
&
18
cm
(v)
9
4
√
3
cm
&
17
cm
Question
4
4.
In the given figure, △HJI is right angled at I. If HI = 9 cm and ∠J = 30°, find HJ
(i)
19
cm
(ii)
18
cm
(iii)
17
cm
(iv)
21
cm
(v)
15
cm
Question
5
5.
In the given figure, △DFE is right angled at E. If DE = 8 cm and ∠F = 30°, find EF
(i)
8
√
3
cm
(ii)
8
√
18
cm
(iii)
24
cm
(iv)
12
√
2
cm
(v)
8
cm
Question
6
6.
In the given figure, △IKJ is right angled at J. If IJ = 9 cm and ∠K = 30°, find IL
(i)
17
4
cm
(ii)
11
2
cm
(iii)
9
2
cm
(iv)
7
2
cm
(v)
5
cm
Question
7
7.
In the given figure, △HJI is right angled at I. If HI = 8 cm and ∠J = 30°, find JK
(i)
11
cm
(ii)
13
cm
(iii)
15
cm
(iv)
12
cm
(v)
9
cm
Question
8
8.
In the given figure, △EGF is right angled at F. If EF = 15 cm and ∠G = 45°, find EG
(i)
30
cm
(ii)
15
cm
(iii)
30
√
3
cm
(iv)
15
√
2
cm
(v)
15
2
√
12
cm
Question
9
9.
In the given figure, △CED is right angled at D. If CD = 15 cm and ∠E = 45°, find DE
(i)
15
cm
(ii)
12
cm
(iii)
14
cm
(iv)
16
cm
(v)
17
cm
Question
10
10.
In the given figure, △DFE is right angled at E. If DE = 15 cm and ∠F = 45°, find DG
(i)
15
2
√
2
cm
(ii)
15
4
√
12
cm
(iii)
15
2
cm
(iv)
15
√
3
cm
(v)
15
cm
Question
11
11.
In the given figure, △HJI is right angled at I. If HI = 16 cm and ∠J = 45°, find JK
(i)
4
√
12
cm
(ii)
16
cm
(iii)
16
√
3
cm
(iv)
8
√
2
cm
(v)
8
cm
Question
12
12.
In the given figure, △DFE is right angled at E. If DE = 21 cm and ∠F = 60°, find DF
(i)
21
√
2
cm
(ii)
14
cm
(iii)
42
cm
(iv)
14
√
18
cm
(v)
14
√
3
cm
Question
13
13.
In the given figure, △CED is right angled at D. If CD = 21 cm and ∠E = 60°, find DE
(i)
21
2
√
2
cm
(ii)
7
cm
(iii)
7
√
3
cm
(iv)
7
√
18
cm
(v)
21
cm
Question
14
14.
In the given figure, △IKJ is right angled at J. If IJ = 24 cm and ∠K = 60°, find IL
(i)
12
√
3
cm
(ii)
12
cm
(iii)
12
√
18
cm
(iv)
36
cm
(v)
18
√
2
cm
Question
15
15.
In the given figure, △DFE is right angled at E. If DE = 25 cm and ∠F = 60°, find FG
(i)
25
6
√
18
cm
(ii)
25
6
√
3
cm
(iii)
25
4
√
2
cm
(iv)
25
2
cm
(v)
25
6
cm
Question
16
16.
A chord of 12 cm subtends an angle of 90° at the centre. Calculate its shortest distance from the centre
(i)
4.0 cm
(ii)
7.0 cm
(iii)
6.0 cm
(iv)
8.0 cm
(v)
5.0 cm
Question
17
17.
An equilateral triangle is inscribed in a circle of radius 10 cm. Find the length of its sides.
(i)
10
√
18
cm
(ii)
10
√
3
cm
(iii)
10
cm
(iv)
15
√
2
cm
(v)
30
cm
Question
18
18.
In the given figure, △DEF is a right angle triangle with ∠F = 90° and EF = 14 cm. R is the mid-point of DF. Find RF
(i)
7
3
cm
(ii)
7
3
√
3
cm
(iii)
7
cm
(iv)
7
2
√
2
cm
(v)
7
3
√
18
cm
Question
19
19.
In the given figure, △HIJ is a right angle triangle with ∠J = 90° and IJ = 13 cm. Q is the mid-point of HJ. Find the length of the altitude from J to HI.
(i)
11
2
cm
(ii)
13
2
cm
(iii)
7
cm
(iv)
15
2
cm
(v)
25
4
cm
Question
20
20.
In the given figure, △ABC is a right angle triangle with ∠C = 90° and BC = 16 cm. T is the mid-point of AC. Find TC
(i)
9
cm
(ii)
10
cm
(iii)
8
cm
(iv)
6
cm
(v)
7
cm
Question
21
21.
In the given figure, △EFG is a right angle triangle with ∠G = 90° and FG = 15 cm. T is the mid-point of EG. Find the length of the altitude from G to EF.
(i)
15
√
3
cm
(ii)
15
2
√
2
cm
(iii)
15
2
cm
(iv)
15
4
√
12
cm
(v)
15
cm
Question
22
22.
In the given figure, △GHI is a right angle triangle with ∠I = 90° and HI = 16 cm. T is the mid-point of GI. Find TI
(i)
12
√
2
cm
(ii)
8
cm
(iii)
8
√
3
cm
(iv)
24
cm
(v)
8
√
18
cm
Question
23
23.
In the given figure, △IJK is a right angle triangle with ∠K = 90° and JK = 15 cm. T is the mid-point of IK. Find the length of the altitude from K to IJ.
(i)
45
4
√
2
cm
(ii)
45
2
cm
(iii)
15
2
√
18
cm
(iv)
15
2
cm
(v)
15
2
√
3
cm
Question
24
24.
In the given figure, if
FH
−
GH
=
2 cm
,
and
FG = 6 cm
,
find
sin
F
(i)
6
5
(ii)
4
7
(iii)
2
5
(iv)
4
5
(v)
4
3
Question
25
25.
In the given figure, if
BD
−
CD
=
2 cm
,
and
BC = 10 cm
,
find
cos
B
(i)
1
3
(ii)
5
13
(iii)
7
13
(iv)
5
11
(v)
3
13
Question
26
26.
In the given figure, if
CE
−
DE
=
2 cm
,
and
CD = 8 cm
,
find
tan
C
(i)
13
8
(ii)
5
2
(iii)
15
8
(iv)
17
8
(v)
3
2
Question
27
27.
In the given figure, if
IK
+
JK
=
50 cm
,
and
IJ = 10 cm
,
find
sin
I
(i)
10
13
(ii)
4
5
(iii)
14
13
(iv)
12
11
(v)
12
13
Question
28
28.
In the given figure, if
HJ
+
IJ
=
18 cm
,
and
HI = 6 cm
,
find
cos
H
(i)
1
(ii)
3
7
(iii)
3
5
(iv)
1
5
Question
29
29.
In the given figure, if
BD
+
CD
=
50 cm
,
and
BC = 10 cm
,
find
tan
B
(i)
2
(ii)
14
5
(iii)
4
(iv)
12
7
(v)
12
5
Question
30
30.
The altitude
AD
of
△ABC
in which
∠A
is obtuse is
9 cm
.
If
BD = 9 cm
and
CD
=
9
√
3
cm
,
find
∠BAC
(i)
120°
(ii)
115°
(iii)
100°
(iv)
105°
(v)
110°
Question
31
31.
In the given figure, △DEF is right angled at E. If EF = 10 cm and ∠F = 30°, find DE and DF
(i)
10
3
4
√
3
cm
&
20
cm
(ii)
10
3
√
3
cm
&
20
3
√
3
cm
(iii)
10
3
4
√
3
cm
&
22
cm
(iv)
10
3
4
√
3
cm
&
20
3
√
3
cm
(v)
10
3
4
√
1
3
cm
&
22
cm
Question
32
32.
In the given figure, △JKL is right angled at K. If KL = 9 cm and ∠L = 45°, find JK and JL
(i)
9
cm
&
9
√
2
cm
(ii)
10
cm
&
20
cm
(iii)
7
cm
&
20
cm
(iv)
10
cm
&
18
cm
(v)
10
cm
&
9
√
2
cm
Question
33
33.
In the given figure, △EFG is right angled at F. If FG = 11 cm and ∠G = 60°, find EF and EG
(i)
11
4
√
3
cm
&
21
cm
(ii)
11
4
√
3
cm
&
22
cm
(iii)
11
4
√
1
3
cm
&
23
cm
(iv)
11
4
√
3
cm
&
23
cm
(v)
11
√
3
cm
&
22
cm
Question
34
34.
In the given figure, △ACB is right angled at B. If AB = 7 cm and ∠C = 30°, find AC
(i)
13
cm
(ii)
14
cm
(iii)
15
cm
(iv)
11
cm
(v)
16
cm
Question
35
35.
In the given figure, △EGF is right angled at F. If EF = 8 cm and ∠G = 30°, find FG
(i)
8
√
3
cm
(ii)
8
√
18
cm
(iii)
8
cm
(iv)
24
cm
(v)
12
√
2
cm
Question
36
36.
In the given figure, △HJI is right angled at I. If HI = 8 cm and ∠J = 30°, find HK
(i)
3
cm
(ii)
4
cm
(iii)
1
cm
(iv)
6
cm
(v)
5
cm
Question
37
37.
In the given figure, △DFE is right angled at E. If DE = 8 cm and ∠F = 30°, find FG
(i)
11
cm
(ii)
10
cm
(iii)
12
cm
(iv)
13
cm
(v)
15
cm
Question
38
38.
In the given figure, △FHG is right angled at G. If FG = 12 cm and ∠H = 45°, find FH
(i)
12
cm
(ii)
24
√
3
cm
(iii)
24
cm
(iv)
6
√
12
cm
(v)
12
√
2
cm
Assignment Key
1) (iv)
2) (v)
3) (ii)
4) (ii)
5) (i)
6) (iii)
7) (iv)
8) (iv)
9) (i)
10) (i)
11) (iv)
12) (v)
13) (iii)
14) (i)
15) (ii)
16) (iii)
17) (ii)
18) (ii)
19) (ii)
20) (iii)
21) (ii)
22) (iii)
23) (v)
24) (iv)
25) (ii)
26) (iii)
27) (v)
28) (iii)
29) (v)
30) (iv)
31) (ii)
32) (i)
33) (v)
34) (ii)
35) (i)
36) (ii)
37) (iii)
38) (v)
