Geometry Answers

1. In a right triangle, the bisector of the right angle divides the hypotenuse in the ratio of 3:5. Determine the measures of the acute angles of the triangle.
2. The lengths of the sides of a triangle are in the ratio of 17:10:9. Find the lengths of the three sides if the area of the triangle is 576cm^2.
3. In an acute triangle ABC, an altitude AD is drawn. Find the area of triangle ABC if AB = 15 inches, AC = 18 inches and BD = 10 inches.
4. Given triangle ABC whose sides are AB = 15 inches, AC = 25 inches and BC = 30 inches. From a point D on side AB, a line DE is drawn to a point E on side AC such that angle ADE is equal to angle ABC. If the perimeter of triangle ADE is 28 inches. Find the lengths of line segments BD and CE.

1. Find the area of a triangle if its two side measure 6 inches and 9 inches, and the bisector of the angle between the sides is 4 square root of 3 inches.
2. In a right triangle, a line perpendicular to the hypotenuse drawn from the midpoint of one of the sides divides the hypotenuse into segments which are 10 cm and 6 cm long. Find the lengths of the two sides of the triangle.
3. The base of an isosceles triangle and the altitude drawn from one of the congruent sides are equal to 18 cm and 15 cm, respectively. Find the lengths of the sides of the triangle.

1. The ratio of the base of an isosceles triangle to its altitude is 3:4. Find the measures of the angles of the triangle.
2. Two altitudes of an isosceles triangle are equal to 20 cm and 30 cm. Determine the possible measures of the base angles of the triangle.
3. The area of a triangle is equal to 48cm^2 and two of its sides measure 12 cm and 9 cm, respectively. Find the possible measures of the included angles of the given sides.

Find the area of a square shown to the right. 27.4 The area is km, km2. Type a whole number or a decimal. Round to the nearest tenth as needed.

Can a sphere be trisected from the center to the surface in three equal volumes?

a trough 15 m long and has bottom 30 cm and 60 cm. its cross-section is a trapezium. find its volume

In a triangle ABC, E is the midpoint of BC and D is a point on AB such that AD : DB = 2 : 1. If CD and AE intersect at P, determine the ratio CP : PD.

Theorem 3-9 states that in a plane,two lines perpendicular to the same line are parallel.Explain why the phrase "in a plane" is needed

Find the perimeter of the figure. https://ka-perseus-graphie.s3.amazonaws.com/eb8635a8059b2c69ad19bf8d44f5a7a7885cf622.png

Let ABC be a triangle with angle A = 90 and AB = AC. Let D and E be points on the segment
BC such that BD : DE : EC = 3 : 5 : 4. Prove that angle DAE = 45.