1. In a ΔABC, if 4∠A = 3∠B = 12∠C, find ∠A? A. 22.5° B. 90° C. 67.5° D. 112.5° Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option C Solution: $$\eqalign{ & 4\angle A = 3\angle B = 12\angle C \cr & A:B:C = \frac{1}{4}:\frac{1}{3}:\frac{1}{{12}} \cr & A:B:C = 3:4:1 \cr & {\text{Now}} \cr & 3x + 4x + x = 180 \cr & 8x = 180 \cr & x = \frac{{180}}{8} \cr & \angle A = 3x = \frac{{180}}{8} \times 3 = 67.5 \cr} $$
2. In ΔPQR Measure of angle Q at is 90°. If sinP = $$\frac{{12}}{{13}}$$ and PQ = 1 cm. Then what is the value of cotR =? A. 2.4 B. 2.6 C. 3 D. 4 Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option A Solution: $$\eqalign{ & 5{\text{ unit}} \to 1\,{\text{cm}} \cr & {\text{1 unit}} \to \frac{1}{5}\,{\text{cm}} \cr & \cot R = \frac{{2.4}}{1} = 2.4\,{\text{cm}} \cr} $$
3. If 0 ≤ θ ≤ $$\frac{\pi }{2}$$ and sec2θ + tan2θ = 7, then θ is A. $$\frac{{5\pi }}{{12}}$$ radian B. $$\frac{\pi }{3}$$ radian C. $$\frac{\pi }{6}$$ radian D. $$\frac{\pi }{2}$$ radian Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B Solution: sec2θ + tan2θ = 7 1 + tan2θ + tan2θ = 7 2tan2θ = 7 - 1 = 6 tan2θ = 3 tanθ = √3 = tan 60° $$\eqalign{ & \because {180^ \circ } = \pi {\text{ radian}} \cr & \therefore {60^ \circ } = \frac{\pi }{{180}} \times 60 = \frac{\pi }{3}{\text{ radian}} \cr} $$
4. In ΔDEF Measure of angle E is 90°. If cosD = $$\frac{5}{{13}}$$ and DE = 1 cm. Then what is Length of side EF? A. 2.6 B. 2.4 C. 1.5 D. 2 Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B Solution: $$\eqalign{ & 5\,{\text{unit}} \to 1\,{\text{cm}} \cr & 1\,{\text{unit}} \to \frac{1}{5}\,{\text{cm}} \cr & {\text{EF}} = 2.4\,{\text{cm}} \cr} $$
5. In ΔDEF Measure of angle E is 90°. If cotD = $$\frac{8}{{15}}$$ and DE = 16 cm. Then what is the Length of side EF? A. 34 B. 15 C. 30 D. 14 Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option C Solution: 8 unit → 16 cm 1 unit → 2 cm EF = 30 cm
6. In circular measure, the value of the angle 11°15' is: A. $$\frac{{{\pi ^c}}}{{16}}$$ B. $$\frac{{{\pi ^c}}}{8}$$ C. $$\frac{{{\pi ^c}}}{4}$$ D. $$\frac{{{\pi ^c}}}{{12}}$$ Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option A Solution: $$\eqalign{ & {11^ \circ }15' = 11 + \frac{{15}}{{60}} = 11 + \frac{1}{4} = \frac{{{{45}^ \circ }}}{4} \cr & {\text{We know }}\pi \,{\text{radian}} = {180^ \circ } \cr & {1^ \circ } = \left( {\frac{\pi }{{180}}} \right){\text{ radian,}} \cr & \frac{{{{45}^ \circ }}}{4} = \frac{\pi }{{{{180}^ \circ }}} \times \frac{{{{45}^ \circ }}}{4} = \frac{{{\pi ^c}}}{{16}} \cr} $$
7. ΔABC is right angle at B. If m∠C = 45°. Then find the value of (cosecA - $$\sqrt 3 $$ ) =? A. $$\frac{{4 - \sqrt 3 }}{2}$$ B. $$\sqrt 2 - \sqrt 3 $$ C. $$ - \frac{{\sqrt 3 }}{2}$$ D. $$\frac{{\sqrt 6 - 1}}{{\sqrt 3 }}$$ Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B Solution: $$\eqalign{ & {\text{cosec}}A - \sqrt 3 \cr & = \frac{{\sqrt 2 x}}{x} - \sqrt 3 \cr & = \sqrt 2 - \sqrt 3 \cr} $$
8. ΔDEF is right angled at E. If ∠D = 45°, then what is the value of cosecFcotD? A. $$\frac{1}{{\sqrt 2 }}$$ B. $$2$$ C. $$\frac{1}{2}$$ D. $$\sqrt 2 $$ Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option D Solution: $$\eqalign{ & \Rightarrow {\text{cosec F}} \times \cot {\text{D}} \cr & = {\text{cosec 4}}{{\text{5}}^ \circ } \times \cot {45^ \circ } \cr & = \sqrt 2 \times 1 \cr & = \sqrt 2 \cr} $$
9. In ΔXYZ Measure of angle Y is 90° if secX = $$\frac{{17}}{8}$$ and XY = 0.8 cm. Then what is Length of side XZ? A. 1.7 B. 1.5 C. 2 D. 2.5 Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option A Solution: XY = 0.8 cm 8 unit → 0.8 cm 1 unit → $$\frac{1}{{10}}$$ XZ = 1.7 cm
10. The measures of the four angles of a quadrilateral are in the ratio 1 : 2 : 4 : 5. What is the measure the biggest angle? A. 120 B. 30 C. 60 D. 150 Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option D Solution: The sum of a quadrilateral is 360° x + 2x + 4x + 5x = 360° 12x = 360° x = 30° Biggest angle = 5x = 5 × 30° = 150°