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 = 10 cm and ∠K = 30°, find IJ and IK
(i)
10
3
√
3
cm
&
20
3
√
3
cm
(ii)
10
3
4
√
3
cm
&
23
cm
(iii)
10
3
4
√
1
3
cm
&
23
cm
(iv)
10
3
4
√
3
cm
&
20
cm
(v)
10
3
4
√
3
cm
&
20
3
√
3
cm
Question
2
2.
In the given figure, △DEF is right angled at E. If EF = 12 cm and ∠F = 45°, find DE and DF
(i)
13
cm
&
24
cm
(ii)
12
cm
&
12
√
2
cm
(iii)
11
cm
&
26
cm
(iv)
13
cm
&
12
√
2
cm
(v)
13
cm
&
26
cm
Question
3
3.
In the given figure, △EFG is right angled at F. If FG = 11 cm and ∠G = 60°, find EF and EG
(i)
11
cm
&
24
cm
(ii)
11
√
3
cm
&
22
cm
(iii)
11
4
√
3
cm
&
22
cm
(iv)
11
4
√
3
cm
&
24
cm
(v)
11
4
√
3
cm
&
21
cm
Question
4
4.
In the given figure, △BDC is right angled at C. If BC = 9 cm and ∠D = 30°, find BD
(i)
16
cm
(ii)
18
cm
(iii)
17
cm
(iv)
20
cm
(v)
19
cm
Question
5
5.
In the given figure, △HJI is right angled at I. If HI = 7 cm and ∠J = 30°, find IJ
(i)
7
√
18
cm
(ii)
7
√
3
cm
(iii)
21
2
√
2
cm
(iv)
21
cm
(v)
7
cm
Question
6
6.
In the given figure, △ACB is right angled at B. If AB = 7 cm and ∠C = 30°, find AD
(i)
4
cm
(ii)
9
2
cm
(iii)
7
2
cm
(iv)
13
4
cm
(v)
5
2
cm
Question
7
7.
In the given figure, △CED is right angled at D. If CD = 9 cm and ∠E = 30°, find EF
(i)
25
2
cm
(ii)
27
2
cm
(iii)
29
2
cm
(iv)
27
4
cm
(v)
27
cm
Question
8
8.
In the given figure, △CED is right angled at D. If CD = 12 cm and ∠E = 45°, find CE
(i)
24
cm
(ii)
12
√
2
cm
(iii)
12
cm
(iv)
6
√
12
cm
(v)
24
√
3
cm
Question
9
9.
In the given figure, △ACB is right angled at B. If AB = 13 cm and ∠C = 45°, find BC
(i)
12
cm
(ii)
14
cm
(iii)
16
cm
(iv)
10
cm
(v)
13
cm
Question
10
10.
In the given figure, △IKJ is right angled at J. If IJ = 15 cm and ∠K = 45°, find IL
(i)
15
2
cm
(ii)
15
√
3
cm
(iii)
15
4
√
12
cm
(iv)
15
2
√
2
cm
(v)
15
cm
Question
11
11.
In the given figure, △CED is right angled at D. If CD = 14 cm and ∠E = 45°, find EF
(i)
14
√
3
cm
(ii)
14
cm
(iii)
7
√
2
cm
(iv)
7
2
√
12
cm
(v)
7
cm
Question
12
12.
In the given figure, △BDC is right angled at C. If BC = 23 cm and ∠D = 60°, find BD
(i)
23
√
2
cm
(ii)
46
cm
(iii)
46
3
cm
(iv)
46
3
√
3
cm
(v)
46
3
√
18
cm
Question
13
13.
In the given figure, △ACB is right angled at B. If AB = 28 cm and ∠C = 60°, find BC
(i)
28
cm
(ii)
28
3
√
3
cm
(iii)
28
3
cm
(iv)
14
√
2
cm
(v)
28
3
√
18
cm
Question
14
14.
In the given figure, △FHG is right angled at G. If FG = 27 cm and ∠H = 60°, find FI
(i)
81
4
√
2
cm
(ii)
27
2
cm
(iii)
27
2
√
18
cm
(iv)
27
2
√
3
cm
(v)
81
2
cm
Question
15
15.
In the given figure, △FHG is right angled at G. If FG = 23 cm and ∠H = 60°, find HI
(i)
23
6
√
3
cm
(ii)
23
2
cm
(iii)
23
6
√
18
cm
(iv)
23
6
cm
(v)
23
4
√
2
cm
Question
16
16.
A chord of 11 cm subtends an angle of 90° at the centre. Calculate its shortest distance from the centre
(i)
7.5 cm
(ii)
5.5 cm
(iii)
6.5 cm
(iv)
4.5 cm
(v)
3.5 cm
Question
17
17.
An equilateral triangle is inscribed in a circle of radius 11 cm. Find the length of its sides.
(i)
33
cm
(ii)
11
√
3
cm
(iii)
11
√
18
cm
(iv)
33
2
√
2
cm
(v)
11
cm
Question
18
18.
In the given figure, △FGH is a right angle triangle with ∠H = 90° and GH = 17 cm. R is the mid-point of FH. Find RH
(i)
17
2
cm
(ii)
17
6
√
18
cm
(iii)
17
6
√
3
cm
(iv)
17
6
cm
(v)
17
4
√
2
cm
Question
19
19.
In the given figure, △BCD is a right angle triangle with ∠D = 90° and CD = 17 cm. R is the mid-point of BD. Find the length of the altitude from D to BC.
(i)
33
4
cm
(ii)
9
cm
(iii)
17
2
cm
(iv)
15
2
cm
(v)
19
2
cm
Question
20
20.
In the given figure, △IJK is a right angle triangle with ∠K = 90° and JK = 16 cm. T is the mid-point of IK. Find TK
(i)
11
cm
(ii)
9
cm
(iii)
5
cm
(iv)
7
cm
(v)
8
cm
Question
21
21.
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)
15
√
3
cm
(ii)
15
cm
(iii)
15
2
√
2
cm
(iv)
15
2
cm
(v)
15
4
√
12
cm
Question
22
22.
In the given figure, △IJK is a right angle triangle with ∠K = 90° and JK = 16 cm. Q is the mid-point of IK. Find QK
(i)
12
√
2
cm
(ii)
8
cm
(iii)
8
√
18
cm
(iv)
24
cm
(v)
8
√
3
cm
Question
23
23.
In the given figure, △CDE is a right angle triangle with ∠E = 90° and DE = 14 cm. S is the mid-point of CE. Find the length of the altitude from E to CD.
(i)
21
2
√
2
cm
(ii)
7
cm
(iii)
7
√
3
cm
(iv)
7
√
18
cm
(v)
21
cm
Question
24
24.
In the given figure, if
DF
−
EF
=
2 cm
,
and
DE = 8 cm
,
find
sin
D
(i)
13
17
(ii)
15
19
(iii)
1
(iv)
15
17
Question
25
25.
In the given figure, if
BD
−
CD
=
2 cm
,
and
BC = 8 cm
,
find
cos
B
(i)
8
19
(ii)
8
15
(iii)
8
17
(iv)
6
17
(v)
10
17
Question
26
26.
In the given figure, if
HJ
−
IJ
=
2 cm
,
and
HI = 8 cm
,
find
tan
H
(i)
3
2
(ii)
5
2
(iii)
17
8
(iv)
13
8
(v)
15
8
Question
27
27.
In the given figure, if
CE
+
DE
=
32 cm
,
and
CD = 8 cm
,
find
sin
C
(i)
15
17
(ii)
15
19
(iii)
1
(iv)
13
17
Question
28
28.
In the given figure, if
FH
+
GH
=
50 cm
,
and
FG = 10 cm
,
find
cos
F
(i)
3
13
(ii)
5
11
(iii)
5
13
(iv)
7
13
(v)
1
3
Question
29
29.
In the given figure, if
AC
+
BC
=
32 cm
,
and
AB = 8 cm
,
find
tan
A
(i)
5
2
(ii)
15
8
(iii)
13
8
(iv)
3
2
(v)
17
8
Question
30
30.
The altitude
EH
of
△EFG
in which
∠E
is obtuse is
6 cm
.
If
FH = 6 cm
and
GH
=
6
√
3
cm
,
find
∠FEG
(i)
100°
(ii)
120°
(iii)
110°
(iv)
115°
(v)
105°
Question
31
31.
In the given figure, △GHI is right angled at H. If HI = 12 cm and ∠I = 30°, find GH and GI
(i)
4
√
3
cm
&
8
√
3
cm
(ii)
4
cm
&
27
cm
(iii)
4
4
√
3
cm
&
8
√
3
cm
(iv)
4
4
√
3
cm
&
27
cm
(v)
4
4
√
3
cm
&
24
cm
Question
32
32.
In the given figure, △ABC is right angled at B. If BC = 12 cm and ∠C = 45°, find AB and AC
(i)
10
cm
&
27
cm
(ii)
13
cm
&
24
cm
(iii)
12
cm
&
12
√
2
cm
(iv)
13
cm
&
27
cm
(v)
13
cm
&
12
√
2
cm
Question
33
33.
In the given figure, △ABC is right angled at B. If BC = 11 cm and ∠C = 60°, find AB and AC
(i)
11
4
√
1
3
cm
&
24
cm
(ii)
11
4
√
3
cm
&
21
cm
(iii)
11
4
√
3
cm
&
24
cm
(iv)
11
√
3
cm
&
22
cm
(v)
11
4
√
3
cm
&
22
cm
Question
34
34.
In the given figure, △HJI is right angled at I. If HI = 8 cm and ∠J = 30°, find HJ
(i)
16
cm
(ii)
14
cm
(iii)
17
cm
(iv)
19
cm
(v)
15
cm
Question
35
35.
In the given figure, △DFE is right angled at E. If DE = 7 cm and ∠F = 30°, find EF
(i)
7
√
18
cm
(ii)
7
cm
(iii)
7
√
3
cm
(iv)
21
cm
(v)
21
2
√
2
cm
Question
36
36.
In the given figure, △BDC is right angled at C. If BC = 9 cm and ∠D = 30°, find BE
(i)
9
2
cm
(ii)
17
4
cm
(iii)
7
2
cm
(iv)
5
cm
(v)
11
2
cm
Question
37
37.
In the given figure, △BDC is right angled at C. If BC = 9 cm and ∠D = 30°, find DE
(i)
25
2
cm
(ii)
27
cm
(iii)
27
4
cm
(iv)
27
2
cm
(v)
29
2
cm
Question
38
38.
In the given figure, △FHG is right angled at G. If FG = 16 cm and ∠H = 45°, find FH
(i)
32
√
3
cm
(ii)
32
cm
(iii)
16
cm
(iv)
16
√
2
cm
(v)
8
√
12
cm
Assignment Key
1) (i)
2) (ii)
3) (ii)
4) (ii)
5) (ii)
6) (iii)
7) (ii)
8) (ii)
9) (v)
10) (iv)
11) (iii)
12) (iv)
13) (ii)
14) (iv)
15) (i)
16) (ii)
17) (ii)
18) (iii)
19) (iii)
20) (v)
21) (iii)
22) (v)
23) (iii)
24) (iv)
25) (iii)
26) (v)
27) (i)
28) (iii)
29) (ii)
30) (v)
31) (i)
32) (iii)
33) (iv)
34) (i)
35) (iii)
36) (i)
37) (iv)
38) (iv)
