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, △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
4
√
3
cm
&
22
cm
(iii)
10
3
4
√
3
cm
&
20
3
√
3
cm
(iv)
10
3
√
3
cm
&
20
3
√
3
cm
(v)
10
3
cm
&
22
cm
Question
2
2.
In the given figure, △GHI is right angled at H. If HI = 9 cm and ∠I = 45°, find GH and GI
(i)
10
cm
&
18
cm
(ii)
8
cm
&
20
cm
(iii)
10
cm
&
20
cm
(iv)
10
cm
&
9
√
2
cm
(v)
9
cm
&
9
√
2
cm
Question
3
3.
In the given figure, △ABC is right angled at B. If BC = 12 cm and ∠C = 60°, find AB and AC
(i)
12
4
√
3
cm
&
26
cm
(ii)
12
cm
&
26
cm
(iii)
12
√
3
cm
&
24
cm
(iv)
12
4
√
3
cm
&
24
cm
(v)
12
4
√
3
cm
&
23
cm
Question
4
4.
In the given figure, △DFE is right angled at E. If DE = 9 cm and ∠F = 30°, find DF
(i)
15
cm
(ii)
19
cm
(iii)
21
cm
(iv)
17
cm
(v)
18
cm
Question
5
5.
In the given figure, △BDC is right angled at C. If BC = 9 cm and ∠D = 30°, find CD
(i)
27
2
√
2
cm
(ii)
27
cm
(iii)
9
√
18
cm
(iv)
9
cm
(v)
9
√
3
cm
Question
6
6.
In the given figure, △BDC is right angled at C. If BC = 9 cm and ∠D = 30°, find BE
(i)
5
cm
(ii)
11
2
cm
(iii)
7
2
cm
(iv)
17
4
cm
(v)
9
2
cm
Question
7
7.
In the given figure, △GIH is right angled at H. If GH = 9 cm and ∠I = 30°, find IJ
(i)
27
cm
(ii)
27
2
cm
(iii)
25
2
cm
(iv)
27
4
cm
(v)
29
2
cm
Question
8
8.
In the given figure, △ACB is right angled at B. If AB = 16 cm and ∠C = 45°, find AC
(i)
32
√
3
cm
(ii)
32
cm
(iii)
16
cm
(iv)
16
√
2
cm
(v)
8
√
12
cm
Question
9
9.
In the given figure, △FHG is right angled at G. If FG = 15 cm and ∠H = 45°, find GH
(i)
14
cm
(ii)
16
cm
(iii)
12
cm
(iv)
15
cm
(v)
17
cm
Question
10
10.
In the given figure, △FHG is right angled at G. If FG = 12 cm and ∠H = 45°, find FI
(i)
6
√
2
cm
(ii)
12
√
3
cm
(iii)
12
cm
(iv)
6
cm
(v)
3
√
12
cm
Question
11
11.
In the given figure, △GIH is right angled at H. If GH = 12 cm and ∠I = 45°, find IJ
(i)
12
√
3
cm
(ii)
6
cm
(iii)
3
√
12
cm
(iv)
12
cm
(v)
6
√
2
cm
Question
12
12.
In the given figure, △BDC is right angled at C. If BC = 27 cm and ∠D = 60°, find BD
(i)
18
cm
(ii)
18
√
3
cm
(iii)
27
√
2
cm
(iv)
18
√
18
cm
(v)
54
cm
Question
13
13.
In the given figure, △ACB is right angled at B. If AB = 24 cm and ∠C = 60°, find BC
(i)
8
√
3
cm
(ii)
12
√
2
cm
(iii)
8
cm
(iv)
24
cm
(v)
8
√
18
cm
Question
14
14.
In the given figure, △HJI is right angled at I. If HI = 22 cm and ∠J = 60°, find HK
(i)
11
√
3
cm
(ii)
33
2
√
2
cm
(iii)
11
cm
(iv)
11
√
18
cm
(v)
33
cm
Question
15
15.
In the given figure, △CED is right angled at D. If CD = 23 cm and ∠E = 60°, find EF
(i)
23
4
√
2
cm
(ii)
23
6
√
18
cm
(iii)
23
6
√
3
cm
(iv)
23
2
cm
(v)
23
6
cm
Question
16
16.
A chord of 17 cm subtends an angle of 90° at the centre. Calculate its shortest distance from the centre
(i)
8.5 cm
(ii)
10.5 cm
(iii)
7.5 cm
(iv)
9.5 cm
(v)
6.5 cm
Question
17
17.
An equilateral triangle is inscribed in a circle of radius 12 cm. Find the length of its sides.
(i)
12
√
18
cm
(ii)
12
√
3
cm
(iii)
18
√
2
cm
(iv)
36
cm
(v)
12
cm
Question
18
18.
In the given figure, △BCD is a right angle triangle with ∠D = 90° and CD = 13 cm. Q is the mid-point of BD. Find QD
(i)
13
2
cm
(ii)
13
6
√
18
cm
(iii)
13
6
cm
(iv)
13
6
√
3
cm
(v)
13
4
√
2
cm
Question
19
19.
In the given figure, △ABC is a right angle triangle with ∠C = 90° and BC = 17 cm. P is the mid-point of AC. Find the length of the altitude from C to AB.
(i)
15
2
cm
(ii)
33
4
cm
(iii)
19
2
cm
(iv)
17
2
cm
(v)
9
cm
Question
20
20.
In the given figure, △BCD is a right angle triangle with ∠D = 90° and CD = 13 cm. S is the mid-point of BD. Find SD
(i)
11
2
cm
(ii)
13
2
cm
(iii)
15
2
cm
(iv)
25
4
cm
(v)
7
cm
Question
21
21.
In the given figure, △EFG is a right angle triangle with ∠G = 90° and FG = 13 cm. S is the mid-point of EG. Find the length of the altitude from G to EF.
(i)
13
2
cm
(ii)
13
cm
(iii)
13
√
3
cm
(iv)
13
2
√
2
cm
(v)
13
4
√
12
cm
Question
22
22.
In the given figure, △EFG is a right angle triangle with ∠G = 90° and FG = 13 cm. T is the mid-point of EG. Find TG
(i)
13
2
√
3
cm
(ii)
13
2
√
18
cm
(iii)
39
2
cm
(iv)
39
4
√
2
cm
(v)
13
2
cm
Question
23
23.
In the given figure, △FGH is a right angle triangle with ∠H = 90° and GH = 14 cm. R is the mid-point of FH. Find the length of the altitude from H to FG.
(i)
21
2
√
2
cm
(ii)
7
cm
(iii)
7
√
3
cm
(iv)
21
cm
(v)
7
√
18
cm
Question
24
24.
In the given figure, if
HJ
−
IJ
=
2 cm
,
and
HI = 10 cm
,
find
sin
H
(i)
12
11
(ii)
14
13
(iii)
4
5
(iv)
12
13
(v)
10
13
Question
25
25.
In the given figure, if
FH
−
GH
=
2 cm
,
and
FG = 6 cm
,
find
cos
F
(i)
1
5
(ii)
3
7
(iii)
1
(iv)
3
5
Question
26
26.
In the given figure, if
GI
−
HI
=
2 cm
,
and
GH = 8 cm
,
find
tan
G
(i)
15
8
(ii)
17
8
(iii)
13
8
(iv)
5
2
(v)
3
2
Question
27
27.
In the given figure, if
IK
+
JK
=
32 cm
,
and
IJ = 8 cm
,
find
sin
I
(i)
15
17
(ii)
13
17
(iii)
15
19
(iv)
1
Question
28
28.
In the given figure, if
HJ
+
IJ
=
50 cm
,
and
HI = 10 cm
,
find
cos
H
(i)
5
13
(ii)
1
3
(iii)
7
13
(iv)
3
13
(v)
5
11
Question
29
29.
In the given figure, if
JL
+
KL
=
18 cm
,
and
JK = 6 cm
,
find
tan
J
(i)
2
3
(ii)
4
(iii)
4
5
(iv)
2
(v)
4
3
Question
30
30.
The altitude
BE
of
△BCD
in which
∠B
is obtuse is
7 cm
.
If
CE = 7 cm
and
DE
=
7
√
3
cm
,
find
∠CBD
(i)
110°
(ii)
105°
(iii)
100°
(iv)
115°
(v)
120°
Question
31
31.
In the given figure, △GHI is right angled at H. If HI = 8 cm and ∠I = 30°, find GH and GI
(i)
8
3
4
√
1
3
cm
&
18
cm
(ii)
8
3
√
3
cm
&
16
3
√
3
cm
(iii)
8
3
4
√
3
cm
&
16
3
√
3
cm
(iv)
8
3
4
√
3
cm
&
18
cm
(v)
8
3
4
√
3
cm
&
16
cm
Question
32
32.
In the given figure, △FGH is right angled at G. If GH = 11 cm and ∠H = 45°, find FG and FH
(i)
12
cm
&
22
cm
(ii)
11
cm
&
11
√
2
cm
(iii)
12
cm
&
25
cm
(iv)
12
cm
&
11
√
2
cm
(v)
10
cm
&
25
cm
Question
33
33.
In the given figure, △BCD is right angled at C. If CD = 8 cm and ∠D = 60°, find BC and BD
(i)
8
4
√
1
3
cm
&
17
cm
(ii)
8
4
√
3
cm
&
16
cm
(iii)
8
4
√
3
cm
&
17
cm
(iv)
8
√
3
cm
&
16
cm
(v)
8
4
√
3
cm
&
15
cm
Question
34
34.
In the given figure, △HJI is right angled at I. If HI = 8 cm and ∠J = 30°, find HJ
(i)
17
cm
(ii)
18
cm
(iii)
16
cm
(iv)
15
cm
(v)
14
cm
Question
35
35.
In the given figure, △BDC is right angled at C. If BC = 9 cm and ∠D = 30°, find CD
(i)
9
√
3
cm
(ii)
9
cm
(iii)
27
cm
(iv)
9
√
18
cm
(v)
27
2
√
2
cm
Question
36
36.
In the given figure, △CED is right angled at D. If CD = 7 cm and ∠E = 30°, find CF
(i)
4
cm
(ii)
5
2
cm
(iii)
7
2
cm
(iv)
9
2
cm
(v)
13
4
cm
Question
37
37.
In the given figure, △CED is right angled at D. If CD = 7 cm and ∠E = 30°, find EF
(i)
19
2
cm
(ii)
21
4
cm
(iii)
21
2
cm
(iv)
21
cm
(v)
23
2
cm
Question
38
38.
In the given figure, △EGF is right angled at F. If EF = 12 cm and ∠G = 45°, find EG
(i)
12
√
2
cm
(ii)
24
√
3
cm
(iii)
24
cm
(iv)
12
cm
(v)
6
√
12
cm
Assignment Key
1) (iv)
2) (v)
3) (iii)
4) (v)
5) (v)
6) (v)
7) (ii)
8) (iv)
9) (iv)
10) (i)
11) (v)
12) (ii)
13) (i)
14) (i)
15) (iii)
16) (i)
17) (ii)
18) (iv)
19) (iv)
20) (ii)
21) (iv)
22) (i)
23) (iii)
24) (iv)
25) (iv)
26) (i)
27) (i)
28) (i)
29) (v)
30) (ii)
31) (ii)
32) (ii)
33) (iv)
34) (iii)
35) (i)
36) (iii)
37) (iii)
38) (i)
