Opposite & Adjacent Sides in a Right Angled Triangle

Q. In the given figure, $∆$ ABC is an equilateral traingle. Points F, D and E are midpoints of side AB, side BC, side AC respectively. Show that $∆$FED is an equilateral traingle.

Q.

In the given triangle, The value of SinA is

1. sin A =$\frac{BC}{AC}$

2. sin A =$\frac{AB}{AC}$

3. sin A =$\frac{BC}{AB}$

4. sin A =1

Q.

Inradius of a circle which is inscribed in an isosceles triangle one of whose angle is $\frac{2\pi }{3}$, is $\sqrt{3}$, then the area of the triangle is

1. $4\sqrt{3}$

2. $12–7\sqrt{3}$

3. $12+7\sqrt{3}$

4. None of these

Q.

In Fig. T is a point on side QR of △PQR and S is a point such that RT = ST. Prove that PQ + PR > QS

Q.

If cos 3A = 0 and A is acute , find the value of

(i) sin A (ii) cos 2A

1. (i) $\frac{1}{\sqrt{2}}$ (ii) $\sqrt{2}$

2. (i) 30° (ii) 60°

3. (i) $\frac{1}{2}$ (ii) $\frac{1}{2}$

4. ( i) $\frac{1}{\sqrt{3}}$ (ii) $\sqrt{3}$

Q.

Question 1
Show that in a right angled triangle, the hypotenuse is the longest side.

Q. Which of the following statements hold true for a quadrilateral ABCD?

1. $sin\left(\frac{A+B}{4}\right)=cot\left(\frac{C+D}{4}\right)$
2. $sin\left(\frac{A+B}{4}\right)=cos\left(\frac{C+D}{4}\right)$
3. $tan\left(\frac{A+C}{4}\right)=cot\left(\frac{B+D}{4}\right)$
4. $tan\left(\frac{A+C}{4}\right)=cos\left(\frac{B+D}{4}\right)$

Q. Question 7 (i)
ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
D is the mid-point of AC.

Q. a triangle ABC right angled at C and D is the mid point of BC. prove that AB^2 =4AD^2 -3AC^2.

Q.

Simplify: $\frac{cose{c}^{2}A}{1+co{t}^{2}A}$ [1 MARK]

Q.

$△ABC$ , right angled at B, BC = 6 cm and ∠ABC = ${30}^{\circ }$. Determine the length of the side AB and AC.

1. 6$\sqrt{3}$ cm , 12cm

2. 4$\sqrt{3}$ cm , 12cm

3. 2$\sqrt{3}$ cm , 16cm

4. $\sqrt{3}$ cm , 16cm

Q. In the given figure, if D is the mid-point of the hypotenuse AC of right \bigtriangleup ABC, if AB is 4 cm and BC is 3 cm, then BD is equalto

Q.

If A = 15°

Find 4 cos 2A . sin 4A .tan 3A - 1

1. 3

2. 2

3. 4

4. 0

Q.

The cotangent of an angle in a right-angled triangle is defined as

1. the ratio between the lengths of the hypotenuse side of an angle to its opposite side.

2. the ratio between the lengths of the adjacent side of an angle to its hypotenuse

3. the ratio between the lengths of the adjacent side of an angle to its opposite side.

4. The ratio between the lengths of the opposite side of an angle to its adjacent side.

Q.

Which of the following statement is correct?

1. $tan({90}^{\circ }-A)=cotA$

2. Both A and B

3. None of the above

4. $cos({90}^{\circ }-A)=sinA$

Q. ∆ABC and ∆DBC are two isosceles triangles on the same base BC. Show that ∠ABD = ∠ACD.

Q.

In the figure given above, what is the value of $tan\theta$ in terms of a, b and c?

1. $\frac{b}{a}$

2. $\frac{a}{b}$

3. $\frac{b}{c}$

4. $\frac{c}{a}$

Q.

The value of cot $\theta$ in the given right triangle is

1. 1

2. $\sqrt{2}$

3. $\frac{1}{\sqrt{2}}$

4. $\frac{1}{2}$

Q.

In $△$ ABC, right angled at B, $\angle$ACB = ${60}^{\circ }$, Values of sec C and cosec C are :

1. Sec C = $\frac{AC}{AB}$ , Cosec C = $\frac{AC}{AB}$

2. Sec C = $\frac{AC}{BC}$ , Cosec C = $\frac{AC}{AB}$

3. Sec C = $\frac{AC}{BC}$ , Cosec C = $\frac{AC}{BC}$

4. Sec C = $\frac{AC}{AB}$ , Cosec C = $\frac{AC}{BC}$

Q. What is the value of tan(P) if P is 45 degree?

1. 0.5
2. 0.86
3. 1
4. \N

Q. If $\Delta ABC$ is right angled at C, then cos B = ___.

1. $\frac{AC}{AB}$
2. $\frac{AC}{BC}$
3. $\frac{AB}{BC}$
4. $\frac{BC}{AB}$

Q. In a right triangle, the longest side is known as?

1. None of the above
2. Perpendicular
3. Hypotenuse
4. Base

Q.

A triangle has base length 7 cm. Its base angle is ${60}^{\circ }$ and the sum of its other 2 sides is 14 cm. What type of triangle is this?

1. Equilateral Triangle

2. Scalene triangle

3. Isoceles Triangle

4. Right Triangle

Q.

In the figure given above, what is the value of $tan\theta$ in terms of a, b and c?

1. $\frac{a}{b}$

2. $\frac{b}{a}$

3. $\frac{b}{c}$

4. $\frac{c}{a}$

Q.

In triangle ABC, right angled at B, if $\angle$A is made smaller and smaller till it becomes zero, what can you say about BC and AC if AB = 1 unit

1. 1, 1

2. 1, 0

3. 0, 1

4. 0, 0

Q.
ABCD is a rectangle such that $\angle CAB={60}^{\circ }$ and $AC=aunits$.
Find the area of rectangle ABCD.

Q. $(\csc 2A-2)(\cot 3A-1)=0$

Q.

In a right ∆, the ratio between the lengths of the the opposite side to the hypotenuse is known as

1. sine

2. cosecant

3. cosine

4. tangent

Q. If $b=3,c=4,\angle B=\frac{\pi }{3}$, then the number of triangles that can be constructed is

1. $0$
2. $3$
3. $1$
4. $2$

Q. If $\tan \theta =\frac{4}{3}$ then $(\sin \theta +\cos \theta )=$

1. $\frac{7}{3}$
2. $\frac{7}{4}$
3. $\frac{7}{5}$
4. $\frac{5}{7}$