Right Angle Triangle

Q. The three angles of a triangle are in the ratio 1 : 2 : 1. Find the angles of the triangle . Classify the triangle on basis of their angles.

Q. The sides of some triangles are given below. Find out which ones are right-angled triangles?
(i) 8, 15, 17
(ii) 11, 12, 15
(iii) 11, 60, 61
(iv) 1.5, 1.6, 1.7
(v) 40, 20, 30

Q.

One angle of a triangle is ${61}^{\circ }$ and the other two angles are in the ratio $\left(\frac{3}{2}\right):\left(\frac{4}{3}\right)$. Find the smallest angle in the triangle.

1. ${61}^{\circ }$

2. ${63}^{\circ }$

3. ${56}^{\circ }$

4. ${59}^{\circ }$

Q.

Which of the following triplet are the sides of right angled triangle?

1. 2, 4, 5

2. 1, 2, 3

3. 3, 4, 5

4. 3, 4, 6

Q. In ∆abc a=6cm b=4.5cm find length of hypotenuse..

Q.

Consider a right angled triangle ABC, right angled at B .Length of AC=5cm.<A=37.The sides of triangles are integers. Find sum of AB, BC and <C .

(In this Question I found the missing angle but is there any method by which we can find the sides (Pythagoras Triplets) or we have to remember some basic ones like 3, 4and 5 in this question?)

Q.

1) ABC is a triangle, right angled at C if AB=25cm and AC=7cm find BC.

Q. The angle between the external bisectors of two angles of a triangle is ${50}^{\circ }$ then the third angle is

1. ${75}^{\circ }$
2. ${80}^{\circ }$
3. ${85}^{\circ }$
4. ${90}^{\circ }$

Q. In right ∆ ABC, the lengths of the legs are given. Find the length of the hypotenuse.
(i) a = 6 cm, b = 8 cm
(ii) a = 8 cm, b = 15 cm
(iii) a = 3 cm, b = 4 cm
(iv) a = 2 cm, b = 1.5 cm

Q. Find all the angles of an equilateral triangle.

1. ${60}^0,{60}^0,{60}^0$
2. ${120}^0,{30}^0,{30}^0$
3. ${90}^0,{30}^0,{60}^0$
4. ${90}^0,{45}^0,{45}^0$

Q. A man goes 3 km due north and then 4 km due east. How far is he away from his initial position?

Q. Which of the following can be classified as right-angled triangles?

1. $\angle 1={45}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={90}^{\circ }$
2. $\angle 1={25}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={110}^{\circ }$
3. $\angle 1={50}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={90}^{\circ }$
4. $\angle 1={50}^{\circ }$; $\angle 2={90}^{\circ }$; $\angle 3={40}^{\circ }$

Q.

In the figure below, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of $\angle$ POS and $\angle$ SOQ respectively. If $\angle$ POS = $x$, then find $\angle$ ROT.

1. ${90}^{\circ }$

2. ${120}^{\circ }$

3. ${75}^{\circ }$

4. ${180}^{\circ }$

Q. A man goes 35 m due west and then 12 m due north. How far is he from the starting point?

Q. The two legs of a right triangle are equal and the square of the hypotenuse is 50. Find the length of each leg.

Q.

Akanchha measured the angles in a triangle. They came out to be ${60}^{\circ },{80}^{\circ }$, and ${70}^{\circ }$ respectively. Now she wants to know what type of triangle it is.
Can you tell what type of triangle it is?

1. Acute angled triangle

2. Obtuse angled triangle

3. Right angled triangle

4. Reflex angled triangle

Q. A ladder 50 dm long when set against the wall of a house just reaches a window at a height of 48 dm. How far is the lower end of the ladder from the base of the wall?

Q. Let the line segment AB and CD intersect at O in such a way that OA=OD and OB=OC then AC=BD, but AC may not be parallel to BD.

1. True
2. False

Q. While calculating the two acute angles of a right angled triangle, Rehaan found them to be measuring ${60}^{\circ }$ and ${20}^{\circ }$ while Kavya found them to be measuring ${65}^{\circ }$ and ${25}^{\circ }$ .
Select the correct statement from the following:

1. Kavya's measurement is accurate while Rehaan's is not.
2. Rehaan's measurement is accurate while Kavya's is not.
3. Both have measured correctly.
4. Both have measured incorrectly.

Q.

Which of the following can form the three sides of a right-angled triangle?

1. AB+BC+CA > 2AM

2. AB+BC+CA < 2AM

3. AB+BC+CA = AM

4. AB+BC+CA = 2 AM

Q.

5cm, 12cm can be two sides of a right-angled triangle.

1. True

2. False

Q.

The two legs of a right triangle are equal and the square of its hypotenuse is $50cm$. Find the length of each leg.

Q. $\Delta ABC$ is right angled at A. AB = 60 units, AC = 80 units and BC = 100 units. D is a point between B and C such that $\Delta ADB$ and $\Delta ADC$ have equal perimeters. What is the length of BD?

1. 10 units
2. 20 units
3. 40 units
4. 60 units

Q. $\Delta ABC$ is right angled at A. AB = 60 units, AC = 80 units and BC = 100 units. D is a point between B and C such that $\Delta ADB$ and $\Delta ADC$ have equal perimeters. What is the length of BD?

1. 20 units
2. 10 units
3. 40 units
4. 60 units

Q. Which of the following can be classified as right angled triangles?

1. $\angle 1={45}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={90}^{\circ }$
2. $\angle 1={25}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={110}^{\circ }$
3. $\angle 1={50}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={90}^{\circ }$
4. $\angle 1={50}^{\circ }$; $\angle 2={90}^{\circ }$; $\angle 3={40}^{\circ }$

Q.

In the given figure, AB = AC. Side BA is produced to D such that BA = AD. $△$BDC is _______.

1. an acute angle triangle

2. an obtuse angle triangle

3. an equilateral triangle

4. a right angle triangle

Q. While calculating the two acute angles of a right angled triangle, Rehaan found them to be measuring = ${60}^{\circ }$ and ${20}^{\circ }$ while Kavya found them to be measuring = ${65}^{\circ }$ and ${25}^{\circ }$ .
Select the correct statement from the following:

1. Kavya's measurement is accurate while Rehaan's is not.
2. Both have measured correctly
3. Rehaan's measurement is accurate while Kavya's is not.
4. Both have measured incorrectly.

Q.

In the figure below, OP, OQ, OR and OS are four rays. Then, find $\frac{(\angle POQ+\angle QOR+\angle SOR+\angle POS)}{3}$.

1. ${60}^{\circ }$

2. ${120}^{\circ }$

3. ${90}^{\circ }$

4. $0^{\circ }$

Q. In triangle $ABC,\angle B={90}^0$ and $D$ is mid-point of $BC$. Prove that: $A{C}^2=A{D}^2+3C{D}^2$

Q.

In an isosceles triangle $\mathrm{AB}=\mathrm{AC}$ and $\mathrm{BA}$ is produced to $\mathrm{D}$, such that $\mathrm{AB}=\mathrm{AD}$ then $\angle \mathrm{BCD}$ is

1. $70°$

2. $90°$

3. $60°$

4. $45°$