Tangent Ratio Worksheet

Tangent Ratio Worksheet
  • Page 1
 1.  
Find the value of tan 90° .
a.
2
b.
π2
c.
d.
1


Solution:

Tan 90° = + ∞


Correct answer : (3)
 2.  
Range of tan x is
a.
R-
b.
R+
c.
R
d.
None of the above


Solution:

Range of tan x is the set of all real numbers, R.


Correct answer : (3)
 3.  
Relationship between tan θ and cot θ is
a.
tan θ . cot θ = 1
b.
tan2 θ + cot2 θ = 1
c.
tan θ + cot θ = 1
d.
tan θcot θ = 1


Solution:

(tan θ) (cot θ) = 1


Correct answer : (1)
 4.  
In ΔABC, tan A =

a.
BC AC.
b.
AB BC.
c.
BC AB.
d.
AB AC.


Solution:

tan A =  leg opposite to Aleg adjacent to A
[Definition.]

tan A = BC / AB
[Substitute.]


Correct answer : (3)
 5.  
In ΔABC, the leg opposite to C is

a.
AC
b.
AB
c.
BC
d.
BC or AC


Solution:

In ΔABC, the leg opposite to C is AB.


Correct answer : (2)
 6.  
In ΔPQR, if x = 13, y = 12 and z = 5 then find the value tan P.

a.
5 13.
b.
5 12.
c.
12 13.
d.
12 5.


Solution:

Tangent of P = leg opposite Pleg adjacent to P
[Definition.]

tan P = 12 / 5
[Substitute.]


Correct answer : (4)
 7.  
In ΔRST, find tan R × tan T. [Given x = 8, y = 15 and z = 17.]

a.
64 225
b.
17
c.
225 64
d.
1


Solution:

tangent of R = leg opposite Rleg adjacent to R
[Definition.]

tan R = 15 / 8
[Substitute.]

tangent of T = leg opposite Tleg adjacent to T
[Definition.]

tan T = 815
[Substitute.]

tan R × tan T = 158 × 815 = 1
[Substitute and simplify.]


Correct answer : (4)
 8.  
Relationship between tan P and tan R is [Given x = 8 and y = 15.]

a.
tan P + tan R = 1
b.
tan Ptan R = 1
c.
tan P × tan R = 1
d.
tan P - tan R = 1


Solution:

tan P = QR / PQ and tan R = PQ / QR
[Use the tangent ratio.]

tan P × tan R = QR / PQ × PQ / QR = 1
[Substitute and simplify.]


Correct answer : (3)
 9.  
Find B in ΔBAC.


a.
Tan-1(12)
b.
1 radian
c.
45°
d.


Solution:

tan B = AC / AB
[Use the tangent ratio.]

AC = AB
[Given.]

tan B = AC / AB
[Substitute.]

tan B = 1

B = 45°
[tan 45° = 1.]


Correct answer : (3)
 10.  
The slope of line l is [Given a = 18 and b = 24.]

a.
3
b.
3 4
c.
4
d.
4 3


Solution:

Slope of a line = tan θ, θ is inclination
[Formula.]

Slope of line l = tan θ = AB / OB
[Use the tangent ratio.]

Slope = 18 / 24 = 3 / 4
[Substitute.]


Correct answer : (2)

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