Basics of Geometry

Q.

In ∆ABC, ∠B = 90°, BC =5 cm, and AC - AB = 1. Evaluate $\frac{1+SinC}{1+CosC}$

Q.

In $△ABC$, right angled at C, AC = 4 cm and $\angle BAC={60}^o$, find the length of side BC.

1. 5√3cm

2. √3
   
   

3. 4√3cm

4. 3 cm

Q.

$△PQR$, right-angled at Q, if PR = 24 cm, QR = 12 cm, then find the value of $\angle QRP$.

1. 30^o

2. 60^o

3. 45^o

4. 90^o

Q. A man on top of a building observes a car at an angle of depression $\alpha$, where $tan\alpha =\frac{1}{\sqrt{5}}$ and sees that it is moving towards the base of the building. Ten minutes later the angle of depression of the car is found to be $\beta$ where tan $\beta =\sqrt{5}$. If the car is moving with an uniform speed, then how much more time will it take to reach the base of the tower?

Q. Lines PQ and RS are parallel. It is given that $\angle RSP={52}^{\circ }$, then find $\angle SPQ$.

1. ${38}^{\circ }$
2. ${45}^{\circ }$
3. ${48}^{\circ }$
4. ${52}^{\circ }$

Q. Lines PQ and RS are parallel. It is given that $\angle RSP={52}^{\circ }$, then find $\angle SPQ$.

1. ${52}^{\circ }$
2. ${45}^{\circ }$
3. ${48}^{\circ }$
4. ${38}^{\circ }$

Q. Lines PQ and RS are parallel. It is given that $\angle RSP={52}^{\circ }$, then find $\angle SPQ$.

1. ${52}^{\circ }$
2. ${38}^{\circ }$
3. ${45}^{\circ }$
4. ${48}^{\circ }$

Q.

From a point 30 m away from the foot of a tower, if the angle of elevation of the top of the tower is 45°, then the height of the tower is ___m.

1. 45

2. 17.32

3. 30

4. 51.96

Q. In a triangle ABC, right angled at B, if AB = 3 cm, BC = 4 cm, then the value of AC (in cm) is .

1. 2
2. 3
3. 4
4. 5

Q. In t$\Delta$ ABC, AB > AC. E is the mid-point of BC and AD is perpendicular to BC. Then,
Answer: $A{B}^2+A{C}^2=2A{E}^2+2B{E}^2$
State whether the above statement is true=1 or false=0.

Q. Lines PQ and RS are parallel. It is given that $\angle RSP={52}^{\circ }$, then find $\angle SPQ$.

1. ${52}^{\circ }$
2. ${45}^{\circ }$
3. ${38}^{\circ }$
4. ${48}^{\circ }$

Q. In a right angled triangle, if one of the angles is 45 degrees, then the lengths of opposite and adjacent sides to the angle are equal.

1. True
2. False

Q. In $△ABC$, $\angle B=90$, $AB=8cm$ and $BC=6cm$. The length of the median BM is

1. 3 cm
2. 5 cm
3. 4 cm
4. 7 cm