Pedal Triangle Properties

Questions and Answers

A triangle inscribed in a given triangle whose vertices are the feet of the three perpendiculars to the sides from the same point insie, the given triangle.

Inscribed triangle

Primitive Triangle

c. Pedal Triangle (correct)

Obtuse Triangl

Sin A cos B – cos A sin B is equivalent to:

Cos (A-B) (correct)

Tan (A-B)

Cot (A-B)

Sin (A-B)

How many degrees is 4800 mils?

270 deg (correct)

180 deg

90 deg

215 deg

The radius of the circle whose arc of length 15 cm makes an angle of ¾ radian at the center is:

11.25 cm Signup and view all the answers

If sin A = 2.511x, cos A = 3.06x and sin²A = 3.939x, find the value of x.

0.256 Signup and view all the answers

Solve for x if tan 3x = 5 tan x.

20.705 deg Signup and view all the answers

If tan x = 1/2, tan y = 1/3, what is the value of tan (x + y)?

1 Signup and view all the answers

The height of the monument is:

33.51 m Signup and view all the answers

The triangle with minimum perimeter but maximum area inscribed in another triangle is known as:

Pedal Triangle Signup and view all the answers

If the sides of the triangle are 2x + 3, x² + 3x + 3, and x² + 2x, find the greatest interior angle of the triangle.

120 deg Signup and view all the answers

Given the sides of a triangle as 3m and 5m. The third side is:

Between 3m and 8m Signup and view all the answers

Given triangle ABC in which A= 30°30', b= 100 m, and c = 200 m, find the length of side a.

124.64 m Signup and view all the answers

An isosceles right triangle has a perimeter of 17.071. Compute the area of the triangle in square units.

10.5 Signup and view all the answers

The area of an isosceles triangle is 36 m² with a 30° included angle of the two adjacent equal sides. Compute the perimeter of the triangle.

30.21 Signup and view all the answers

To determine the width of a river, a surveyor measures a line AB 120 m long on one bank. To a point C on the other bank he determines the angle BAC = 48°36' and the angle ABC = 54°42'. Find the width of the river.

55.7 Signup and view all the answers

The angle which the line of sight to the object makes with the horizontal is above the eye of an observer.

Angle of elevation Signup and view all the answers

The intersection of the medians of the triangle is called:

Incenter Signup and view all the answers

Which of the following is not a property of a triangle?

If the two sides are equal, the angles opposite are unequal. Signup and view all the answers

What is the sum of the squares of the sine and cosine of an angle?

1 Signup and view all the answers

If the coverged sin θ = 0.134, what is the value of θ?

30° Signup and view all the answers

The angle or inclination of ascend of a road having 8.25% grade is degrees?

4.27 Signup and view all the answers

Which of the following cannot be an oblique angle?

Right Signup and view all the answers

Evaluate arc cot[2 cos(arc sin 0.5)].

60 deg Signup and view all the answers

Study Notes

Trigonometry Formulas and Concepts

The formula for the difference of two angles is: sin(A - B) = sin A cos B - cos A sin B
The formula for the sum of two angles is: sin(A + B) = sin A cos B + cos A sin B
The formula for the tangent of the difference of two angles is: tan(A - B) = (tan A - tan B) / (1 + tan A tan B)
The formula for the tangent of the sum of two angles is: tan(A + B) = (tan A + tan B) / (1 - tan A tan B)

Angle of Elevation and Depression

The angle of elevation is the angle between the line of sight and the horizontal when the object is above the observer's eye level.
The angle of depression is the angle between the line of sight and the horizontal when the object is below the observer's eye level.

Solving Triangles

In a right triangle, the Pythagorean theorem can be used to find the length of the hypotenuse: c² = a² + b²
In a triangle, the law of cosines can be used to find the length of a side: c² = a² + b² - 2ab cos C
In a triangle, the law of sines can be used to find the length of a side: a / sin A = b / sin B = c / sin C

Special Right Triangles

A 30-60-90 triangle has angles of 30°, 60°, and 90°, and side lengths in the ratio of 1:√3:2
A 45-45-90 triangle has angles of 45°, 45°, and 90°, and side lengths in the ratio of 1:1:√2

Inverse Trigonometric Functions

The inverse sine function is defined as: sin⁻¹(x) = θ, where sin(θ) = x
The inverse cosine function is defined as: cos⁻¹(x) = θ, where cos(θ) = x
The inverse tangent function is defined as: tan⁻¹(x) = θ, where tan(θ) = x

Applications of Trigonometry

Trigonometry can be used to solve problems involving right triangles, such as finding the height of a building or the distance to a ship at sea.
Trigonometry can be used to solve problems involving oblique triangles, such as finding the area of a triangle or the length of a side.
Trigonometry has many real-world applications, including physics, engineering, navigation, and computer graphics.

Important Values

The value of sin(30°) is 1/2
The value of cos(30°) is √3/2
The value of tan(30°) is 1/√3
The value of sin(45°) is 1/√2
The value of cos(45°) is 1/√2
The value of tan(45°) is 1

Unit Conversions

1 radian is equivalent to 180° / π
1 degree is equivalent to π / 180 radians

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Description

A quiz on the properties of a pedal triangle, formed by the feet of perpendiculars from a point inside a given triangle. Learn about this important concept in geometry!