EduSahara™ Assignment
Name : Trigonometry Diagram Problems
Chapter : Trigonometrical Ratios
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
In the given figure, △FGH is right angled at G. If GH = 10 cm and ∠H = 30°, find FG and FH
(i)
10
3
4
√
3
cm
&
20
3
√
3
cm
(ii)
10
3
√
3
cm
&
20
3
√
3
cm
(iii)
10
3
4
√
3
cm
&
23
cm
(iv)
10
3
4
√
1
3
cm
&
23
cm
(v)
10
3
4
√
3
cm
&
20
cm
Question
2
2.
In the given figure, △BCD is right angled at C. If CD = 11 cm and ∠D = 45°, find BC and BD
(i)
12
cm
&
22
cm
(ii)
9
cm
&
25
cm
(iii)
11
cm
&
11
√
2
cm
(iv)
12
cm
&
11
√
2
cm
(v)
12
cm
&
25
cm
Question
3
3.
In the given figure, △CDE is right angled at D. If DE = 10 cm and ∠E = 60°, find CD and CE
(i)
10
√
3
cm
&
20
cm
(ii)
10
cm
&
21
cm
(iii)
10
4
√
3
cm
&
19
cm
(iv)
10
4
√
3
cm
&
21
cm
(v)
10
4
√
3
cm
&
20
cm
Question
4
4.
In the given figure, △IKJ is right angled at J. If IJ = 8 cm and ∠K = 30°, find IK
(i)
15
cm
(ii)
18
cm
(iii)
14
cm
(iv)
17
cm
(v)
16
cm
Question
5
5.
In the given figure, △HJI is right angled at I. If HI = 9 cm and ∠J = 30°, find IJ
(i)
9
√
18
cm
(ii)
9
√
3
cm
(iii)
9
cm
(iv)
27
cm
(v)
27
2
√
2
cm
Question
6
6.
In the given figure, △CED is right angled at D. If CD = 8 cm and ∠E = 30°, find CF
(i)
5
cm
(ii)
3
cm
(iii)
4
cm
(iv)
2
cm
(v)
6
cm
Question
7
7.
In the given figure, △EGF is right angled at F. If EF = 8 cm and ∠G = 30°, find GH
(i)
10
cm
(ii)
14
cm
(iii)
13
cm
(iv)
12
cm
(v)
11
cm
Question
8
8.
In the given figure, △BDC is right angled at C. If BC = 13 cm and ∠D = 45°, find BD
(i)
26
√
3
cm
(ii)
13
√
2
cm
(iii)
13
cm
(iv)
26
cm
(v)
13
2
√
12
cm
Question
9
9.
In the given figure, △BDC is right angled at C. If BC = 13 cm and ∠D = 45°, find CD
(i)
11
cm
(ii)
12
cm
(iii)
13
cm
(iv)
15
cm
(v)
14
cm
Question
10
10.
In the given figure, △FHG is right angled at G. If FG = 14 cm and ∠H = 45°, find FI
(i)
7
2
√
12
cm
(ii)
14
√
3
cm
(iii)
7
√
2
cm
(iv)
7
cm
(v)
14
cm
Question
11
11.
In the given figure, △IKJ is right angled at J. If IJ = 16 cm and ∠K = 45°, find KL
(i)
8
cm
(ii)
4
√
12
cm
(iii)
16
√
3
cm
(iv)
16
cm
(v)
8
√
2
cm
Question
12
12.
In the given figure, △CED is right angled at D. If CD = 23 cm and ∠E = 60°, find CE
(i)
23
√
2
cm
(ii)
46
3
√
3
cm
(iii)
46
3
cm
(iv)
46
3
√
18
cm
(v)
46
cm
Question
13
13.
In the given figure, △HJI is right angled at I. If HI = 22 cm and ∠J = 60°, find IJ
(i)
22
3
cm
(ii)
22
cm
(iii)
22
3
√
18
cm
(iv)
22
3
√
3
cm
(v)
11
√
2
cm
Question
14
14.
In the given figure, △DFE is right angled at E. If DE = 23 cm and ∠F = 60°, find DG
(i)
69
2
cm
(ii)
23
2
√
3
cm
(iii)
69
4
√
2
cm
(iv)
23
2
√
18
cm
(v)
23
2
cm
Question
15
15.
In the given figure, △GIH is right angled at H. If GH = 27 cm and ∠I = 60°, find IJ
(i)
27
2
cm
(ii)
9
2
cm
(iii)
27
4
√
2
cm
(iv)
9
2
√
18
cm
(v)
9
2
√
3
cm
Question
16
16.
A chord of 16 cm subtends an angle of 90° at the centre. Calculate its shortest distance from the centre
(i)
10.0 cm
(ii)
9.0 cm
(iii)
7.0 cm
(iv)
6.0 cm
(v)
8.0 cm
Question
17
17.
An equilateral triangle is inscribed in a circle of radius 9 cm. Find the length of its sides.
(i)
9
√
3
cm
(ii)
9
√
18
cm
(iii)
27
cm
(iv)
9
cm
(v)
27
2
√
2
cm
Question
18
18.
In the given figure, if
GI
−
HI
=
2 cm
,
and
GH = 10 cm
,
find
sin
G
(i)
4
5
(ii)
12
13
(iii)
12
11
(iv)
10
13
(v)
14
13
Question
19
19.
In the given figure, if
BD
−
CD
=
2 cm
,
and
BC = 6 cm
,
find
cos
B
(i)
1
(ii)
3
7
(iii)
3
5
(iv)
1
5
Question
20
20.
In the given figure, if
FH
−
GH
=
2 cm
,
and
FG = 6 cm
,
find
tan
F
(i)
4
3
(ii)
2
(iii)
2
3
(iv)
4
5
(v)
4
Question
21
21.
In the given figure, if
FH
+
GH
=
32 cm
,
and
FG = 8 cm
,
find
sin
F
(i)
13
17
(ii)
15
19
(iii)
15
17
(iv)
1
Question
22
22.
In the given figure, if
FH
+
GH
=
50 cm
,
and
FG = 10 cm
,
find
cos
F
(i)
5
11
(ii)
1
3
(iii)
5
13
(iv)
3
13
(v)
7
13
Question
23
23.
In the given figure, if
FH
+
GH
=
32 cm
,
and
FG = 8 cm
,
find
tan
F
(i)
17
8
(ii)
15
8
(iii)
13
8
(iv)
3
2
(v)
5
2
Question
24
24.
The altitude
GJ
of
△GHI
in which
∠G
is obtuse is
5 cm
.
If
HJ = 5 cm
and
IJ
=
5
√
3
cm
,
find
∠HGI
(i)
115°
(ii)
120°
(iii)
110°
(iv)
100°
(v)
105°
Assignment Key
1) (ii)
2) (iii)
3) (i)
4) (v)
5) (ii)
6) (iii)
7) (iv)
8) (ii)
9) (iii)
10) (iii)
11) (v)
12) (ii)
13) (iv)
14) (ii)
15) (v)
16) (v)
17) (i)
18) (ii)
19) (iii)
20) (i)
21) (iii)
22) (iii)
23) (ii)
24) (v)
