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, △GHI is right angled at H. If HI = 10 cm and ∠I = 30°, find GH and GI
(i)
10
3
4
√
3
cm
&
20
3
√
3
cm
(ii)
10
3
4
√
3
cm
&
22
cm
(iii)
10
3
4
√
3
cm
&
20
cm
(iv)
10
3
√
3
cm
&
20
3
√
3
cm
(v)
10
3
cm
&
22
cm
Question
2
2.
In the given figure, △FGH is right angled at G. If GH = 11 cm and ∠H = 45°, find FG and FH
(i)
12
cm
&
24
cm
(ii)
12
cm
&
11
√
2
cm
(iii)
11
cm
&
11
√
2
cm
(iv)
9
cm
&
24
cm
(v)
12
cm
&
22
cm
Question
3
3.
In the given figure, △BCD is right angled at C. If CD = 12 cm and ∠D = 60°, find BC and BD
(i)
12
4
√
1
3
cm
&
26
cm
(ii)
12
√
3
cm
&
24
cm
(iii)
12
4
√
3
cm
&
23
cm
(iv)
12
4
√
3
cm
&
26
cm
(v)
12
4
√
3
cm
&
24
cm
Question
4
4.
In the given figure, △BDC is right angled at C. If BC = 7 cm and ∠D = 30°, find BD
(i)
14
cm
(ii)
15
cm
(iii)
17
cm
(iv)
13
cm
(v)
12
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)
27
2
√
2
cm
(iii)
9
cm
(iv)
27
cm
(v)
9
√
3
cm
Question
6
6.
In the given figure, △ACB is right angled at B. If AB = 8 cm and ∠C = 30°, find AD
(i)
4
cm
(ii)
6
cm
(iii)
2
cm
(iv)
3
cm
(v)
5
cm
Question
7
7.
In the given figure, △CED is right angled at D. If CD = 9 cm and ∠E = 30°, find EF
(i)
27
4
cm
(ii)
25
2
cm
(iii)
27
2
cm
(iv)
29
2
cm
(v)
27
cm
Question
8
8.
In the given figure, △ACB is right angled at B. If AB = 14 cm and ∠C = 45°, find AC
(i)
28
cm
(ii)
28
√
3
cm
(iii)
14
√
2
cm
(iv)
7
√
12
cm
(v)
14
cm
Question
9
9.
In the given figure, △DFE is right angled at E. If DE = 13 cm and ∠F = 45°, find EF
(i)
16
cm
(ii)
14
cm
(iii)
12
cm
(iv)
13
cm
(v)
11
cm
Question
10
10.
In the given figure, △BDC is right angled at C. If BC = 15 cm and ∠D = 45°, find BE
(i)
15
cm
(ii)
15
2
√
2
cm
(iii)
15
4
√
12
cm
(iv)
15
√
3
cm
(v)
15
2
cm
Question
11
11.
In the given figure, △HJI is right angled at I. If HI = 13 cm and ∠J = 45°, find JK
(i)
13
2
cm
(ii)
13
cm
(iii)
13
√
3
cm
(iv)
13
2
√
2
cm
(v)
13
4
√
12
cm
Question
12
12.
In the given figure, △IKJ is right angled at J. If IJ = 23 cm and ∠K = 60°, find IK
(i)
23
√
2
cm
(ii)
46
3
√
18
cm
(iii)
46
3
cm
(iv)
46
cm
(v)
46
3
√
3
cm
Question
13
13.
In the given figure, △HJI is right angled at I. If HI = 27 cm and ∠J = 60°, find IJ
(i)
9
√
3
cm
(ii)
27
2
√
2
cm
(iii)
27
cm
(iv)
9
√
18
cm
(v)
9
cm
Question
14
14.
In the given figure, △GIH is right angled at H. If GH = 25 cm and ∠I = 60°, find GJ
(i)
75
4
√
2
cm
(ii)
75
2
cm
(iii)
25
2
cm
(iv)
25
2
√
3
cm
(v)
25
2
√
18
cm
Question
15
15.
In the given figure, △IKJ is right angled at J. If IJ = 24 cm and ∠K = 60°, find KL
(i)
4
√
3
cm
(ii)
6
√
2
cm
(iii)
4
√
18
cm
(iv)
4
cm
(v)
12
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)
6.0 cm
(ii)
8.0 cm
(iii)
7.0 cm
(iv)
5.0 cm
(v)
4.0 cm
Question
17
17.
An equilateral triangle is inscribed in a circle of radius 10 cm. Find the length of its sides.
(i)
30
cm
(ii)
10
√
18
cm
(iii)
15
√
2
cm
(iv)
10
cm
(v)
10
√
3
cm
Question
18
18.
In the given figure, △DEF is a right angle triangle with ∠F = 90° and EF = 13 cm. T is the mid-point of DF. Find TF
(i)
13
6
√
3
cm
(ii)
13
4
√
2
cm
(iii)
13
2
cm
(iv)
13
6
√
18
cm
(v)
13
6
cm
Question
19
19.
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 the length of the altitude from K to IJ.
(i)
5
cm
(ii)
8
cm
(iii)
10
cm
(iv)
9
cm
(v)
7
cm
Question
20
20.
In the given figure, △EFG is a right angle triangle with ∠G = 90° and FG = 14 cm. Q is the mid-point of EG. Find QG
(i)
7
cm
(ii)
10
cm
(iii)
6
cm
(iv)
8
cm
(v)
4
cm
Question
21
21.
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)
14
cm
(ii)
14
√
3
cm
(iii)
7
√
2
cm
(iv)
7
2
√
12
cm
(v)
7
cm
Question
22
22.
In the given figure, △JKL is a right angle triangle with ∠L = 90° and KL = 17 cm. Q is the mid-point of JL. Find QL
(i)
51
2
cm
(ii)
51
4
√
2
cm
(iii)
17
2
√
18
cm
(iv)
17
2
√
3
cm
(v)
17
2
cm
Question
23
23.
In the given figure, △CDE is a right angle triangle with ∠E = 90° and DE = 17 cm. R is the mid-point of CE. Find the length of the altitude from E to CD.
(i)
17
2
cm
(ii)
51
2
cm
(iii)
17
2
√
3
cm
(iv)
51
4
√
2
cm
(v)
17
2
√
18
cm
Question
24
24.
In the given figure, if
AC
−
BC
=
2 cm
,
and
AB = 10 cm
,
find
sin
A
(i)
14
13
(ii)
10
13
(iii)
12
13
(iv)
12
11
(v)
4
5
Question
25
25.
In the given figure, if
JL
−
KL
=
2 cm
,
and
JK = 6 cm
,
find
cos
J
(i)
3
7
(ii)
3
5
(iii)
1
(iv)
1
5
Question
26
26.
In the given figure, if
AC
−
BC
=
2 cm
,
and
AB = 10 cm
,
find
tan
A
(i)
2
(ii)
4
(iii)
12
7
(iv)
12
5
(v)
14
5
Question
27
27.
In the given figure, if
HJ
+
IJ
=
50 cm
,
and
HI = 10 cm
,
find
sin
H
(i)
14
13
(ii)
4
5
(iii)
10
13
(iv)
12
13
(v)
12
11
Question
28
28.
In the given figure, if
GI
+
HI
=
50 cm
,
and
GH = 10 cm
,
find
cos
G
(i)
5
11
(ii)
5
13
(iii)
3
13
(iv)
7
13
(v)
1
3
Question
29
29.
In the given figure, if
FH
+
GH
=
32 cm
,
and
FG = 8 cm
,
find
tan
F
(i)
3
2
(ii)
13
8
(iii)
17
8
(iv)
15
8
(v)
5
2
Question
30
30.
The altitude
BE
of
△BCD
in which
∠B
is obtuse is
9 cm
.
If
CE = 9 cm
and
DE
=
9
√
3
cm
,
find
∠CBD
(i)
120°
(ii)
100°
(iii)
115°
(iv)
105°
(v)
110°
Question
31
31.
In the given figure, △EFG is right angled at F. If FG = 9 cm and ∠G = 30°, find EF and EG
(i)
3
√
3
cm
&
6
√
3
cm
(ii)
3
4
√
3
cm
&
18
cm
(iii)
3
4
√
3
cm
&
6
√
3
cm
(iv)
3
4
√
3
cm
&
21
cm
(v)
3
cm
&
21
cm
Question
32
32.
In the given figure, △BCD is right angled at C. If CD = 10 cm and ∠D = 45°, find BC and BD
(i)
11
cm
&
10
√
2
cm
(ii)
9
cm
&
22
cm
(iii)
11
cm
&
22
cm
(iv)
10
cm
&
10
√
2
cm
(v)
11
cm
&
20
cm
Question
33
33.
In the given figure, △JKL is right angled at K. If KL = 11 cm and ∠L = 60°, find JK and JL
(i)
11
4
√
3
cm
&
22
cm
(ii)
11
cm
&
24
cm
(iii)
11
4
√
3
cm
&
24
cm
(iv)
11
√
3
cm
&
22
cm
(v)
11
4
√
3
cm
&
21
cm
Question
34
34.
In the given figure, △ACB is right angled at B. If AB = 9 cm and ∠C = 30°, find AC
(i)
19
cm
(ii)
16
cm
(iii)
18
cm
(iv)
17
cm
(v)
21
cm
Question
35
35.
In the given figure, △ACB is right angled at B. If AB = 7 cm and ∠C = 30°, find BC
(i)
7
√
3
cm
(ii)
21
cm
(iii)
7
cm
(iv)
7
√
18
cm
(v)
21
2
√
2
cm
Question
36
36.
In the given figure, △CED is right angled at D. If CD = 9 cm and ∠E = 30°, find CF
(i)
7
2
cm
(ii)
9
2
cm
(iii)
17
4
cm
(iv)
11
2
cm
(v)
5
cm
Question
37
37.
In the given figure, △ACB is right angled at B. If AB = 9 cm and ∠C = 30°, find CD
(i)
27
2
cm
(ii)
27
4
cm
(iii)
27
cm
(iv)
29
2
cm
(v)
25
2
cm
Question
38
38.
In the given figure, △HJI is right angled at I. If HI = 16 cm and ∠J = 45°, find HJ
(i)
32
cm
(ii)
8
√
12
cm
(iii)
16
cm
(iv)
32
√
3
cm
(v)
16
√
2
cm
Assignment Key
1) (iv)
2) (iii)
3) (ii)
4) (i)
5) (v)
6) (i)
7) (iii)
8) (iii)
9) (iv)
10) (ii)
11) (iv)
12) (v)
13) (i)
14) (iv)
15) (i)
16) (i)
17) (v)
18) (i)
19) (ii)
20) (i)
21) (iii)
22) (iv)
23) (iii)
24) (iii)
25) (ii)
26) (iv)
27) (iv)
28) (ii)
29) (iv)
30) (iv)
31) (i)
32) (iv)
33) (iv)
34) (iii)
35) (i)
36) (ii)
37) (i)
38) (v)
