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
&
23
cm
(ii)
10
3
cm
&
23
cm
(iii)
10
3
4
√
3
cm
&
20
cm
(iv)
10
3
√
3
cm
&
20
3
√
3
cm
(v)
10
3
4
√
3
cm
&
20
3
√
3
cm
Question
2
2.
In the given figure, △ABC is right angled at B. If BC = 10 cm and ∠C = 45°, find AB and AC
(i)
11
cm
&
23
cm
(ii)
8
cm
&
23
cm
(iii)
11
cm
&
20
cm
(iv)
10
cm
&
10
√
2
cm
(v)
11
cm
&
10
√
2
cm
Question
3
3.
In the given figure, △CDE is right angled at D. If DE = 9 cm and ∠E = 60°, find CD and CE
(i)
9
4
√
1
3
cm
&
20
cm
(ii)
9
√
3
cm
&
18
cm
(iii)
9
4
√
3
cm
&
18
cm
(iv)
9
4
√
3
cm
&
20
cm
(v)
9
4
√
3
cm
&
17
cm
Question
4
4.
In the given figure, △ACB is right angled at B. If AB = 7 cm and ∠C = 30°, find AC
(i)
11
cm
(ii)
15
cm
(iii)
13
cm
(iv)
17
cm
(v)
14
cm
Question
5
5.
In the given figure, △EGF is right angled at F. If EF = 9 cm and ∠G = 30°, find FG
(i)
9
√
18
cm
(ii)
27
2
√
2
cm
(iii)
9
cm
(iv)
9
√
3
cm
(v)
27
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)
7
cm
(iii)
3
cm
(iv)
4
cm
(v)
2
cm
Question
7
7.
In the given figure, △EGF is right angled at F. If EF = 8 cm and ∠G = 30°, find GH
(i)
11
cm
(ii)
12
cm
(iii)
13
cm
(iv)
9
cm
(v)
15
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
cm
(ii)
32
√
3
cm
(iii)
16
√
2
cm
(iv)
16
cm
(v)
8
√
12
cm
Question
9
9.
In the given figure, △HJI is right angled at I. If HI = 13 cm and ∠J = 45°, find IJ
(i)
13
cm
(ii)
14
cm
(iii)
12
cm
(iv)
16
cm
(v)
10
cm
Question
10
10.
In the given figure, △BDC is right angled at C. If BC = 14 cm and ∠D = 45°, find BE
(i)
14
√
3
cm
(ii)
7
2
√
12
cm
(iii)
7
√
2
cm
(iv)
14
cm
(v)
7
cm
Question
11
11.
In the given figure, △GIH is right angled at H. If GH = 14 cm and ∠I = 45°, find IJ
(i)
7
cm
(ii)
14
cm
(iii)
7
√
2
cm
(iv)
7
2
√
12
cm
(v)
14
√
3
cm
Question
12
12.
In the given figure, △DFE is right angled at E. If DE = 27 cm and ∠F = 60°, find DF
(i)
18
cm
(ii)
27
√
2
cm
(iii)
18
√
3
cm
(iv)
18
√
18
cm
(v)
54
cm
Question
13
13.
In the given figure, △GIH is right angled at H. If GH = 24 cm and ∠I = 60°, find HI
(i)
24
cm
(ii)
8
√
18
cm
(iii)
8
√
3
cm
(iv)
12
√
2
cm
(v)
8
cm
Question
14
14.
In the given figure, △GIH is right angled at H. If GH = 22 cm and ∠I = 60°, find GJ
(i)
11
cm
(ii)
11
√
3
cm
(iii)
33
cm
(iv)
11
√
18
cm
(v)
33
2
√
2
cm
Question
15
15.
In the given figure, △BDC is right angled at C. If BC = 23 cm and ∠D = 60°, find DE
(i)
23
2
cm
(ii)
23
6
√
18
cm
(iii)
23
6
cm
(iv)
23
4
√
2
cm
(v)
23
6
√
3
cm
Question
16
16.
A chord of 15 cm subtends an angle of 90° at the centre. Calculate its shortest distance from the centre
(i)
5.5 cm
(ii)
9.5 cm
(iii)
8.5 cm
(iv)
7.5 cm
(v)
6.5 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
cm
(iii)
15
√
2
cm
(iv)
10
√
3
cm
(v)
10
√
18
cm
Question
18
18.
In the given figure, △JKL is a right angle triangle with ∠L = 90° and KL = 17 cm. S is the mid-point of JL. Find SL
(i)
17
2
cm
(ii)
17
6
√
18
cm
(iii)
17
6
√
3
cm
(iv)
17
4
√
2
cm
(v)
17
6
cm
Question
19
19.
In the given figure, △DEF is a right angle triangle with ∠F = 90° and EF = 13 cm. S is the mid-point of DF. Find the length of the altitude from F to DE.
(i)
25
4
cm
(ii)
13
2
cm
(iii)
7
cm
(iv)
15
2
cm
(v)
11
2
cm
Question
20
20.
In the given figure, △HIJ is a right angle triangle with ∠J = 90° and IJ = 16 cm. S is the mid-point of HJ. Find SJ
(i)
11
cm
(ii)
7
cm
(iii)
9
cm
(iv)
8
cm
(v)
6
cm
Question
21
21.
In the given figure, △FGH is a right angle triangle with ∠H = 90° and GH = 16 cm. Q is the mid-point of FH. Find the length of the altitude from H to FG.
(i)
16
√
3
cm
(ii)
16
cm
(iii)
8
√
2
cm
(iv)
8
cm
(v)
4
√
12
cm
Question
22
22.
In the given figure, △CDE is a right angle triangle with ∠E = 90° and DE = 17 cm. P is the mid-point of CE. Find PE
(i)
17
2
√
18
cm
(ii)
51
2
cm
(iii)
17
2
cm
(iv)
17
2
√
3
cm
(v)
51
4
√
2
cm
Question
23
23.
In the given figure, △HIJ is a right angle triangle with ∠J = 90° and IJ = 17 cm. P is the mid-point of HJ. Find the length of the altitude from J to HI.
(i)
17
2
√
18
cm
(ii)
17
2
√
3
cm
(iii)
51
4
√
2
cm
(iv)
51
2
cm
(v)
17
2
cm
Question
24
24.
In the given figure, if
AC
−
BC
=
2 cm
,
and
AB = 6 cm
,
find
sin
A
(i)
6
5
(ii)
2
5
(iii)
4
3
(iv)
4
5
(v)
4
7
Question
25
25.
In the given figure, if
CE
−
DE
=
2 cm
,
and
CD = 8 cm
,
find
cos
C
(i)
8
15
(ii)
10
17
(iii)
8
19
(iv)
8
17
(v)
6
17
Question
26
26.
In the given figure, if
CE
−
DE
=
2 cm
,
and
CD = 10 cm
,
find
tan
C
(i)
12
5
(ii)
14
5
(iii)
2
(iv)
4
(v)
12
7
Question
27
27.
In the given figure, if
GI
+
HI
=
18 cm
,
and
GH = 6 cm
,
find
sin
G
(i)
2
5
(ii)
4
5
(iii)
4
7
(iv)
4
3
(v)
6
5
Question
28
28.
In the given figure, if
BD
+
CD
=
18 cm
,
and
BC = 6 cm
,
find
cos
B
(i)
1
5
(ii)
3
7
(iii)
1
(iv)
3
5
Question
29
29.
In the given figure, if
GI
+
HI
=
50 cm
,
and
GH = 10 cm
,
find
tan
G
(i)
12
7
(ii)
14
5
(iii)
4
(iv)
12
5
(v)
2
Question
30
30.
The altitude
GJ
of
△GHI
in which
∠G
is obtuse is
9 cm
.
If
HJ = 9 cm
and
IJ
=
9
√
3
cm
,
find
∠HGI
(i)
120°
(ii)
100°
(iii)
110°
(iv)
105°
(v)
115°
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
√
3
cm
&
20
3
√
3
cm
(ii)
10
3
4
√
3
cm
&
20
3
√
3
cm
(iii)
10
3
4
√
3
cm
&
20
cm
(iv)
10
3
4
√
3
cm
&
22
cm
(v)
10
3
cm
&
22
cm
Question
32
32.
In the given figure, △IJK is right angled at J. If JK = 9 cm and ∠K = 45°, find IJ and IK
(i)
8
cm
&
20
cm
(ii)
10
cm
&
18
cm
(iii)
10
cm
&
9
√
2
cm
(iv)
10
cm
&
20
cm
(v)
9
cm
&
9
√
2
cm
Question
33
33.
In the given figure, △HIJ is right angled at I. If IJ = 10 cm and ∠J = 60°, find HI and HJ
(i)
10
4
√
1
3
cm
&
22
cm
(ii)
10
4
√
3
cm
&
20
cm
(iii)
10
4
√
3
cm
&
22
cm
(iv)
10
4
√
3
cm
&
19
cm
(v)
10
√
3
cm
&
20
cm
Question
34
34.
In the given figure, △GIH is right angled at H. If GH = 9 cm and ∠I = 30°, find GI
(i)
21
cm
(ii)
16
cm
(iii)
17
cm
(iv)
19
cm
(v)
18
cm
Question
35
35.
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)
8
cm
(iv)
12
√
2
cm
(v)
24
cm
Question
36
36.
In the given figure, △HJI is right angled at I. If HI = 7 cm and ∠J = 30°, find HK
(i)
13
4
cm
(ii)
5
2
cm
(iii)
9
2
cm
(iv)
7
2
cm
(v)
4
cm
Question
37
37.
In the given figure, △IKJ is right angled at J. If IJ = 9 cm and ∠K = 30°, find KL
(i)
27
2
cm
(ii)
27
cm
(iii)
27
4
cm
(iv)
25
2
cm
(v)
29
2
cm
Question
38
38.
In the given figure, △CED is right angled at D. If CD = 14 cm and ∠E = 45°, find CE
(i)
14
cm
(ii)
7
√
12
cm
(iii)
28
√
3
cm
(iv)
28
cm
(v)
14
√
2
cm
Assignment Key
1) (iv)
2) (iv)
3) (ii)
4) (v)
5) (iv)
6) (iv)
7) (ii)
8) (iii)
9) (i)
10) (iii)
11) (iii)
12) (iii)
13) (iii)
14) (ii)
15) (v)
16) (iv)
17) (iv)
18) (iii)
19) (ii)
20) (iv)
21) (iii)
22) (iv)
23) (ii)
24) (iv)
25) (iv)
26) (i)
27) (ii)
28) (iv)
29) (iv)
30) (iv)
31) (i)
32) (v)
33) (v)
34) (v)
35) (i)
36) (iv)
37) (i)
38) (v)
