If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side

Q.

Find the exact values of $\cos 150°$ and $\sin 150°$.

Q. The height of an equilateral triangle is 6cm. Its area Is

Q.

Find the value of $(\sin {30}^{\circ }+\cos {60}^{\circ })$.

Q. The sides of a triangle are 5 cm, 12 cm and 13 cm respectively. The length of the shortest altitude is=

Q. Question 5
In $\Delta PQR$, if $\angle R=\angle P$ and QR =4 cm and PR =5cm. Then, the length of PQ is
(A) 4 cm
(B) 5 cm
(C) 2 cm
(D) 2.5 cm

Q.

Prove that $\tan 75°+cot75°=4$.

Q.

The line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$is parallel to the plane

1. $3x+4y+5z=7$

2. $2x+3y+4z=0$

3. $x+y-z=2$

4. $2x+y-2z=0$

Q.

What is $\sin 360°$ degrees?

Q.

Three forces $\mathrm{P},\mathrm{Q},\mathrm{R}$ are acting at a point in a plane. The angle between $\mathrm{P},\mathrm{Q}$ and $\mathrm{Q},\mathrm{R}$ are $150°$ and $120°$ respectively, then for equilibrium; forces $\mathrm{P},\mathrm{Q},\mathrm{R}$ are in the ratio

1. $1:2:3$

2. $1:2:3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

3. $3:2:1$

4. $3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}:2:1$

Q.

If the angles of a triangle are in the ratio $5:6:7$ . Find the measure of each angle .

Q.

The sides of a triangular plot are in the ratio of 3:5:7 and its perimeter is 300 m. Its area is:

1. $1500\sqrt{2}{m}^2$

2. $1500\sqrt{3}{m}^2$

3. $1425\sqrt{2}{m}^2$

4. $1500m^2$

Q.

The sides of a triangle are $120m,170m,250m.$ Find its area and height of the triangle if the base is $250m.$

Q.

If the height of an equilateral triangle is 6 cm , then find the area of the triangle

Q.

3 mark question

Prove side opposite to greater angle is longer in a triangle.

Q.

ABCD is a rectangle in which diagonal AC bisects angle A as well as angle C. Show that

(1) ABCD is a square

(2) diagonal BD bisects angle B as well as angle D

Q. The area of an isosceles triangle is 12 cm sq . If one of of its equal side is 5 cm, then its base is equal to?

Q. In triangles ABC and PQR, AB = PQ, BC = QR and angle B = angle Q, then they are congruent according to?

1. S.S.S. criteria
2. S.A.S. criteria
3. A.A.A. criteria
4. A.S.A. criteria

Q.

Draw the graph of y = 2x + 4. Use the graph to find the area between the line and the axes.

Q.

How do you prove $\tan \left(90°+x\right)=-cot\left(x\right)$?

Q.

How many non-overlapping triangles can we make in an $n-$gon (polygon having $n$ sides), by joining the vertices?
a) $n-1$
b) $n-2$
c) $n-3$
d) $n-4$

Q. 40. Prove that area of a triangle is 1/2.base.height

Q.

Prove that the Sum of any two sides of a triangle is greater than the third side. Triangle Inequality Theorem.

Q. Define the incircle of a triangle? How can you locate the incenter of a triangle?

Q.

In triangle, $\angle B={90}^{\circ }$, $AB=(2x+1)$ cm and $BC=(x+1)$ cm . If the area of the triangle ABC is $60c{m}^2$ , find its perimeter .

Q.

Which of the following pairs of angles are not complementary angles?

1. 40°, 50°

2. 45°, 45°

3. 60°, 30°

4. 85°, 15°

Q.

If D is any point on the base BC produced, of an isosceles triangle ABC, prove that AD > AB. [3 MARKS]

Q. 13. Three circles each of radius r unit are drawn inside an equilateral triangle of side a units, such that each circle touch the other two and two sides of the triangle as shown in the figure(p, q, r are the centres of the circles).Then relation between r and a is

Q. Question 7
Express $sin{67}^{\circ }+cos{75}^{\circ }$ in terms of trigonometric ratios of angles between $0^{\circ }$ and ${45}^{\circ }$.

Q.

A student is given three sticks of length 15 CM 8 cm and 5 cm respectively his friend asked him to make a triangle with the help of these sticks and then find its area

Q.

If $x=a\left(\cos t+\log \tan \frac{t}{2}\right),y=a\sin t$ then $\frac{dy}{dx}$ is equal to.

1. $\tan t$

2. $-\tan t$

3. $cott$

4. $-cott$