MCQ Questions on Circular Measurement of Angle for Competitive Exams

21

ΔABC is right angled at B. If m∠A = 60° then find the value of (secC + 2).

A) $$\frac{{2 + 2\sqrt 3 }}{{\sqrt 2 }}$$ B) $$\frac{4}{3}$$ C) $$\frac{{2 + 2\sqrt 3 }}{{\sqrt 3 }}$$ D) $$\frac{3}{4}$$

Discuss

Answer & Solution

Answer: Option C

Solution:

$$\eqalign{ & \sec C + 2 \cr & \frac{{2x}}{{\sqrt 3 x}} + 2 \cr} $$
Circular Measurement of Angle mcq question image

$$\eqalign{ & \frac{2}{{\sqrt 3 }} + 2 \cr & \frac{{2 + 2\sqrt 3 }}{{\sqrt 3 }} \cr} $$

22

What is the measure of central angle of the arc. Whose length is 11 cm and radius of the circle is 14 cm?

A) 45° B) 60° C) 75° D) 90°

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & \theta = \frac{l}{r}{\text{ radian}} = \frac{{11}}{{14}}{\text{ radian}} \cr & \because \pi {\text{ radian}} = {180^ \circ } \cr & \therefore 1{\text{ radian}} = \frac{{{{180}^ \circ }}}{\pi } \cr & \therefore \frac{{11}}{{14}}{\text{ radian}} = \frac{{180}}{{\frac{{22}}{7}}} \times \frac{{11}}{{14}} \cr & = \frac{{180 \times 11 \times 7}}{{22 \times 14}} \cr & = {45^ \circ } \cr} $$

23

The circular measure of an angle of an isosceles triangle is $$\frac{{5\pi }}{9}$$, circular measure of one of the other angles must be:

A) $$\frac{{5\pi }}{{18}}$$ B) $$\frac{{5\pi }}{9}$$ C) $$\frac{{2\pi }}{9}$$ D) $$\frac{{4\pi }}{9}$$

Discuss

Answer & Solution

Answer: Option C

No explanation is given for this question. Let's Discuss on Board

24

In ΔPQR measure of angle Q is 90°. If tanP = $$\frac{4}{3}$$ and PQ = 1.5 cm. Then what is the length (in cm) of side PR?

A) 2 B) 2.5 C) 3 D) 4.8

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & \tan {\text{P}} = \frac{4}{3} \cr & 3{\text{ unit}} \to 1.5{\text{ cm}} \cr & 1{\text{ unit}} \to \frac{{1.5}}{3}{\text{ cm}} = .5{\text{ cm}} \cr & {\text{PR}} = 2.5\,{\text{cm}} \cr} $$

25

The measure of the angles of a triangle are in the ratio 2 : 7 : 11. Measures of angles are:

A) 16°, 56°, 88° B) 18°, 63°, 99° C) 20°, 70°, 90° D) 25°, 175°, 105°

Discuss

Answer & Solution

Answer: Option B

Solution:

Angles of triangle are in ratio 2 : 7 : 11
According to question
2x + 7x + 11x = 180
20x = 180
x = 9
Angles of triangle is 18°, 63°, 99°

26

In a right-angled triangle XYZ right-angled at Y. if XY = $$2\sqrt 6 $$ and XZ - YZ = 2, then secX + tanX is:

A) $$\frac{1}{{\sqrt 6 }}$$ B) $$\sqrt 6 $$ C) $$2\sqrt 6 $$ D) $$\frac{{\sqrt 6 }}{2}$$

Discuss

Answer & Solution

Answer: Option B

Solution:

XZ - YZ = 2
h - P = 2 . . . . . . . (i)
h² = (2√6)² + P²
h² - P² = (2√6)²
(h - P)(h + P) = 4 × 6
(2)(h + P) = 24
h + P = 12 . . . . . . . (ii)
Adding equation (i) and (ii)
2h = 14
h = 7, P = 5
$$\eqalign{ & \sec {\text{X}} + \tan {\text{X}} \cr & = \frac{{\text{h}}}{{{\text{XY}}}} + \frac{{\text{P}}}{{{\text{XY}}}} \cr & = \frac{7}{{2\sqrt 6 }} + \frac{5}{{2\sqrt 6 }} \cr & = \frac{{12}}{{2\sqrt 6 }} \cr & = \frac{6}{{\sqrt 6 }} \cr & = \sqrt 6 \cr} $$

27

ΔLMN is right angled at M. If ∠N = 60°, then tanL = . . . . . . . .

A) $$\frac{1}{2}$$ B) $$\frac{1}{{\sqrt 3 }}$$ C) $$\frac{1}{{\sqrt 2 }}$$ D) $$3$$

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\boxed{\tan L = \tan {{30}^ \circ } = \frac{1}{{\sqrt 3 }}}$$