# Right triangle practice problems

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of two of the triangle's sides, which are called the legs of the triangle. The other side of the triangle is called the hypotenuse, which is the side opposite the right angle, and is the longest side of the triangle. Right triangles are important in mathematics and are used in many areas of science and engineering, including trigonometry, physics, and construction. The Pythagorean theorem which states that in a right triangle, the sum of the squares of the legs (a,b) equals the square of the hypotenuse (c) is a fundamental result in geometry.#### Number of problems found: 1640

- Know one angle

In a right-angled triangle, the measure of an angle is 40°. Find the measure of other angles of the triangle in degrees. - The hypotenuse

The hypotenuse of a right-angled triangle is 20 meters. If the difference between the lengths of the other sides is 4 meters, find the other sides. - A right

A right triangle has side lengths a=3, b=5, and c=4, as shown below. Use these lengths to find tan x, sin x, and cos x. - General right triangle

In a right triangle, if a =x+34 and b = x and c= 50, then solve for x. Side c is a hypotenuse. Then discuss the case when a or b is a hypotenuse.

- Prove 2

Prove that the minimum number of straight single cuts/strokes needs to divide a given right-angled triangle or an obtuse-angled triangle into a collection of all acute-angled triangles is seven(7). - A right triangle

A right triangle has legs with lengths of 24 cm and 21 cm if the length of the hypotenuse, in cm, can be written in the form of 3 sqrt(d), then what is the value of d? - An isosceles triangle

An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 18 inches, and the length of the base is 15 in - A triangle 10

A triangle has vertices at (4, 5), (-3, 2), and (-2, 5). What are the coordinates of the vertices of the image after the translation (x, y) arrow-right (x + 3, y - 5)? - Mrs. Clarke

Mrs. Clarke is teaching a 5th-grade class. She is standing 40 feet in front of Valeria. Sarah is sitting to Valeria's right. If Sarah and Mrs. Clarke are 50 feet apart, how far apart are Valeria and Sarah?

- A tree 2

A tree is broken at a height of 6 m from the ground and its top touches the ground at a distance of 8 m from the base of the tree . Find the original height of the tree. - FGH right triangle

Given a right triangle with leg lengths f and g, and hypotenuse h, if f = 7 cm and h = 11.2 cm, what is g? - An equilateral triangle 2

If the sides of an equilateral triangle are increased by 2 meters, the area is increased by 7√3 square meters. Find the length of the side. - A right 3

A right triangle has a perimeter of 300 cm . its hypotenuse is 130cm. What are the lengths of the other sides . - Find area 2

Find the area of the green region in the given picture. Dimensions are shown.

- Missing side length

Use the Pythagorean Theorem (a² + b²=c²) to find a missing side length: a = 5; c = 13 ; b=? - Trigonometric fx

When an acute angle φ is in the standard position, its terminal side passes through point P (1,3). Find trigonometric functions of angle θ : sin φ, cos φ, tan φ, cotan φ. - A radio antenna

Avanti is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 21 meters from the building. The angle of elevation from her eyes to the roof (point A) is 42°, and the angle of elevation from - An electrician 7

An electrician has to repair an electric fault on a pole 4 meters in height. He needs to reach a point 1 m below the top. What should be the length of the ladder that he could use, when inclined at an angle 60° to the horizontal? - Triangle 82

Triangle PQR has vertices located at (2, 2), (5, -4), and (-4, -1). What type of triangle is triangle PQR?

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