# Tangent Ratio Worksheet

Tangent Ratio Worksheet
• Page 1
1.
Find the value of tan 90° .
 a. 2 b. $\frac{\pi }{2}$ c. ∞ d. 1

#### Solution:

Tan 90° = + ∞

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.

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. = 1

#### Solution:

(tan θ) (cot θ) = 1

4.
In ΔABC, tan A =

 a. $\frac{BC}{AC}$. b. $\frac{AB}{BC}$. c. $\frac{BC}{AB}$. d. $\frac{AB}{AC}$.

#### Solution:

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

tan A = BC / AB
[Substitute.]

5.
In ΔABC, the leg opposite to $\angle$C is

 a. $\stackrel{‾}{\mathrm{AC}}$ b. $\stackrel{‾}{\mathrm{AB}}$ c. $\stackrel{‾}{\mathrm{BC}}$ d. $\stackrel{‾}{\mathrm{BC}}$ or $\stackrel{‾}{\mathrm{AC}}$

#### Solution:

In ΔABC, the leg opposite to C is AB.

6.
In ΔPQR, if $x$ = 13, $y$ = 12 and $z$ = 5 then find the value tan $P$.

 a. $\frac{5}{13}$. b. $\frac{5}{12}$. c. $\frac{12}{13}$. d. $\frac{12}{5}$.

#### Solution:

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

tan P = 12 / 5
[Substitute.]

7.
In ΔRST, find tan R × tan T. [Given $x$ = 8, $y$ = 15 and $z$ = 17.]

 a. $\frac{64}{225}$ b. 17 c. $\frac{225}{64}$ 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.]

8.
Relationship between tan P and tan R is [Given $x$ = 8 and $y$ = 15.]

 a. tan P + tan R = 1 b. = 1 c. tan P Ãƒâ€” 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 Ãƒâ€” tan R = QR / PQ Ãƒâ€” PQ / QR = 1
[Substitute and simplify.]

9.
Find $\angle$B in ΔBAC.

 a. ${\mathrm{Tan}}^{-1}\left(12\right)$ b. 1 radian c. 45° d. 1°

#### 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.]

10.
The slope of line $l$ is [Given $a$ = 18 and $b$ = 24.]

 a. 3 b. $\frac{3}{4}$ c. 4 d. $\frac{4}{3}$

#### 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.]