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
√
3
cm
&
20
3
√
3
cm
(iii)
10
3
4
√
1
3
cm
&
22
cm
(iv)
10
3
4
√
3
cm
&
22
cm
(v)
10
3
4
√
3
cm
&
20
cm
Question
2
2.
In the given figure, △JKL is right angled at K. If KL = 9 cm and ∠L = 45°, find JK and JL
(i)
9
cm
&
9
√
2
cm
(ii)
7
cm
&
21
cm
(iii)
10
cm
&
9
√
2
cm
(iv)
10
cm
&
18
cm
(v)
10
cm
&
21
cm
Question
3
3.
In the given figure, △HIJ is right angled at I. If IJ = 9 cm and ∠J = 60°, find HI and HJ
(i)
9
cm
&
20
cm
(ii)
9
√
3
cm
&
18
cm
(iii)
9
4
√
3
cm
&
20
cm
(iv)
9
4
√
3
cm
&
17
cm
(v)
9
4
√
3
cm
&
18
cm
Question
4
4.
In the given figure, △EGF is right angled at F. If EF = 7 cm and ∠G = 30°, find EG
(i)
15
cm
(ii)
17
cm
(iii)
13
cm
(iv)
14
cm
(v)
12
cm
Question
5
5.
In the given figure, △FHG is right angled at G. If FG = 8 cm and ∠H = 30°, find GH
(i)
24
cm
(ii)
8
√
18
cm
(iii)
12
√
2
cm
(iv)
8
cm
(v)
8
√
3
cm
Question
6
6.
In the given figure, △FHG is right angled at G. If FG = 9 cm and ∠H = 30°, find FI
(i)
11
2
cm
(ii)
7
2
cm
(iii)
5
cm
(iv)
17
4
cm
(v)
9
2
cm
Question
7
7.
In the given figure, △EGF is right angled at F. If EF = 9 cm and ∠G = 30°, find GH
(i)
27
cm
(ii)
29
2
cm
(iii)
27
2
cm
(iv)
25
2
cm
(v)
27
4
cm
Question
8
8.
In the given figure, △ACB is right angled at B. If AB = 14 cm and ∠C = 45°, find AC
(i)
7
√
12
cm
(ii)
14
√
2
cm
(iii)
28
cm
(iv)
28
√
3
cm
(v)
14
cm
Question
9
9.
In the given figure, △CED is right angled at D. If CD = 15 cm and ∠E = 45°, find DE
(i)
18
cm
(ii)
15
cm
(iii)
13
cm
(iv)
14
cm
(v)
16
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
cm
(ii)
14
cm
(iii)
14
√
3
cm
(iv)
7
2
√
12
cm
(v)
7
cm
Question
11
11.
In the given figure, △EGF is right angled at F. If EF = 14 cm and ∠G = 45°, find GH
(i)
14
√
3
cm
(ii)
7
√
2
cm
(iii)
7
cm
(iv)
14
cm
(v)
7
2
√
12
cm
Question
12
12.
In the given figure, △FHG is right angled at G. If FG = 24 cm and ∠H = 60°, find FH
(i)
48
cm
(ii)
16
√
3
cm
(iii)
16
√
18
cm
(iv)
16
cm
(v)
24
√
2
cm
Question
13
13.
In the given figure, △BDC is right angled at C. If BC = 27 cm and ∠D = 60°, find CD
(i)
27
2
√
2
cm
(ii)
9
√
18
cm
(iii)
9
cm
(iv)
9
√
3
cm
(v)
27
cm
Question
14
14.
In the given figure, △FHG is right angled at G. If FG = 26 cm and ∠H = 60°, find FI
(i)
13
√
3
cm
(ii)
13
√
18
cm
(iii)
39
cm
(iv)
39
2
√
2
cm
(v)
13
cm
Question
15
15.
In the given figure, △EGF is right angled at F. If EF = 23 cm and ∠G = 60°, find GH
(i)
23
6
√
18
cm
(ii)
23
4
√
2
cm
(iii)
23
6
√
3
cm
(iv)
23
6
cm
(v)
23
2
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)
8.5 cm
(ii)
6.5 cm
(iii)
9.5 cm
(iv)
7.5 cm
(v)
5.5 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)
33
2
√
2
cm
(iv)
11
cm
(v)
11
√
18
cm
Question
18
18.
In the given figure, △IJK is a right angle triangle with ∠K = 90° and JK = 15 cm. R is the mid-point of IK. Find RK
(i)
5
2
√
3
cm
(ii)
15
4
√
2
cm
(iii)
5
2
cm
(iv)
15
2
cm
(v)
5
2
√
18
cm
Question
19
19.
In the given figure, △ABC is a right angle triangle with ∠C = 90° and BC = 15 cm. T is the mid-point of AC. Find the length of the altitude from C to AB.
(i)
17
2
cm
(ii)
29
4
cm
(iii)
13
2
cm
(iv)
15
2
cm
(v)
8
cm
Question
20
20.
In the given figure, △GHI is a right angle triangle with ∠I = 90° and HI = 15 cm. Q is the mid-point of GI. Find QI
(i)
8
cm
(ii)
15
2
cm
(iii)
13
2
cm
(iv)
17
2
cm
(v)
29
4
cm
Question
21
21.
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 the length of the altitude from L to JK.
(i)
17
2
√
2
cm
(ii)
17
4
√
12
cm
(iii)
17
2
cm
(iv)
17
cm
(v)
17
√
3
cm
Question
22
22.
In the given figure, △HIJ is a right angle triangle with ∠J = 90° and IJ = 13 cm. Q is the mid-point of HJ. Find QJ
(i)
39
4
√
2
cm
(ii)
13
2
√
3
cm
(iii)
39
2
cm
(iv)
13
2
cm
(v)
13
2
√
18
cm
Question
23
23.
In the given figure, △GHI is a right angle triangle with ∠I = 90° and HI = 17 cm. P is the mid-point of GI. Find the length of the altitude from I to GH.
(i)
17
2
cm
(ii)
51
2
cm
(iii)
51
4
√
2
cm
(iv)
17
2
√
18
cm
(v)
17
2
√
3
cm
Question
24
24.
In the given figure, if
FH
−
GH
=
2 cm
,
and
FG = 8 cm
,
find
sin
F
(i)
1
(ii)
15
17
(iii)
13
17
(iv)
15
19
Question
25
25.
In the given figure, if
FH
−
GH
=
2 cm
,
and
FG = 10 cm
,
find
cos
F
(i)
5
13
(ii)
1
3
(iii)
3
13
(iv)
5
11
(v)
7
13
Question
26
26.
In the given figure, if
AC
−
BC
=
2 cm
,
and
AB = 6 cm
,
find
tan
A
(i)
4
5
(ii)
4
(iii)
2
(iv)
4
3
(v)
2
3
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)
6
5
(iv)
4
7
(v)
4
3
Question
28
28.
In the given figure, if
EG
+
FG
=
32 cm
,
and
EF = 8 cm
,
find
cos
E
(i)
6
17
(ii)
8
17
(iii)
8
15
(iv)
8
19
(v)
10
17
Question
29
29.
In the given figure, if
JL
+
KL
=
32 cm
,
and
JK = 8 cm
,
find
tan
J
(i)
3
2
(ii)
17
8
(iii)
5
2
(iv)
15
8
(v)
13
8
Question
30
30.
The altitude
CF
of
△CDE
in which
∠C
is obtuse is
3 cm
.
If
DF = 3 cm
and
EF
=
3
√
3
cm
,
find
∠DCE
(i)
120°
(ii)
105°
(iii)
110°
(iv)
115°
(v)
100°
Question
31
31.
In the given figure, △EFG is right angled at F. If FG = 11 cm and ∠G = 30°, find EF and EG
(i)
11
3
4
√
3
cm
&
22
3
√
3
cm
(ii)
11
3
4
√
3
cm
&
22
cm
(iii)
11
3
cm
&
25
cm
(iv)
11
3
√
3
cm
&
22
3
√
3
cm
(v)
11
3
4
√
3
cm
&
25
cm
Question
32
32.
In the given figure, △IJK is right angled at J. If JK = 12 cm and ∠K = 45°, find IJ and IK
(i)
10
cm
&
26
cm
(ii)
13
cm
&
26
cm
(iii)
13
cm
&
24
cm
(iv)
12
cm
&
12
√
2
cm
(v)
13
cm
&
12
√
2
cm
Question
33
33.
In the given figure, △BCD is right angled at C. If CD = 11 cm and ∠D = 60°, find BC and BD
(i)
11
4
√
3
cm
&
22
cm
(ii)
11
4
√
3
cm
&
23
cm
(iii)
11
4
√
1
3
cm
&
23
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)
16
cm
(ii)
19
cm
(iii)
20
cm
(iv)
17
cm
(v)
18
cm
Question
35
35.
In the given figure, △GIH is right angled at H. If GH = 8 cm and ∠I = 30°, find HI
(i)
8
√
18
cm
(ii)
8
cm
(iii)
12
√
2
cm
(iv)
24
cm
(v)
8
√
3
cm
Question
36
36.
In the given figure, △HJI is right angled at I. If HI = 8 cm and ∠J = 30°, find HK
(i)
6
cm
(ii)
3
cm
(iii)
4
cm
(iv)
5
cm
(v)
2
cm
Question
37
37.
In the given figure, △IKJ is right angled at J. If IJ = 7 cm and ∠K = 30°, find KL
(i)
21
cm
(ii)
23
2
cm
(iii)
21
2
cm
(iv)
21
4
cm
(v)
19
2
cm
Question
38
38.
In the given figure, △CED is right angled at D. If CD = 16 cm and ∠E = 45°, find CE
(i)
32
√
3
cm
(ii)
16
cm
(iii)
16
√
2
cm
(iv)
32
cm
(v)
8
√
12
cm
Assignment Key
1) (ii)
2) (i)
3) (ii)
4) (iv)
5) (v)
6) (v)
7) (iii)
8) (ii)
9) (ii)
10) (i)
11) (ii)
12) (ii)
13) (iv)
14) (i)
15) (iii)
16) (iv)
17) (ii)
18) (i)
19) (iv)
20) (ii)
21) (i)
22) (ii)
23) (v)
24) (ii)
25) (i)
26) (iv)
27) (ii)
28) (ii)
29) (iv)
30) (ii)
31) (iv)
32) (iv)
33) (iv)
34) (v)
35) (v)
36) (iii)
37) (iii)
38) (iii)
