Special Right Triangles Assignment and Quiz

The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Check all that apply.

A C

A man is standing near the Washington Monument. At a 60° angle of elevation from the ground, the man sees the top of the 555-foot monument. Which measurements are accurate based on the scenario? Check all that apply.

A. The distance from the man's feet to the base of the monument is 185\(3 feet. B. The distance from the man's feet to the top of the monument is 370\(3 feet.

A person is standing exactly 36 ft from a telephone pole. There is a 30° angle of elevation from the ground to the top of the pole. What is the height of the pole?

B

Consider triangle GHJ. What is the length of line segment HJ?

B

The hypotenuse of a 45°-45°-90° triangle measures 24 inches. What is the length of the one leg of the triangle?

B. 12\(2 in.

Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°-45°-90° triangle) Prove: In a 45°-45°-90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this isosceles triangle becomes a2 + a2 = c2. By combining like terms, 2a2 = c2. Which final step will prove that the length of the hypotenuse, c, is times the length of each leg?

C

Consider triangle PQR. What is the length of side QR?

C

Isaiah sketches a model of a skateboard ramp. The model has two surfaces on which to skate, represented by sides AB and AD in the diagram. The steepest side of the model, AB, measures 4 inches. What is the length of the other skating surface, AD?

C

The height of trapezoid VWXZ is units. The upper base,VW, measures 10 units. Use the 30°-60°-90° triangle theorem to find the length of YX. What is the length of the lower base, ZX?

C

Triangle ABC is an equilateral triangle. Segment AD measures 18 inches. Which statements about the diagram are correct? Check all that apply.

C. DC=6\(3 in. D. AC=12\(3 in.

What are the angle measures in triangle ABC?

C. m∠A = 90°, m∠B = 60°, m∠C = 30°

Consider triangle DEF. The legs have a length of 36 units each. What is the length of the hypotenuse of the triangle

D

Consider triangle QRS. The legs each have a length of 10 units. What is the length of the hypotenuse of the triangle?

D

The hypotenuse of a 45°-45°-90° triangle measures 18 cm. What is the length of one leg of the triangle?

D

The roof of a house is the shape of an isosceles right triangle as shown in the diagram below. What is the height of the roof, h?

B. 5\(2 ft

From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?

B. 5\(3/3 ft

A wall in Maria's bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle. Using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall.

C

Consider that △ABC is an equilateral triangle, and AD is a perpendicular bisector of △ABC. If AB = 2x, complete the statements below. 2 + (AD)2 = (2x)2 (AD)2 = x2 - x2 (AD)2 = x2 AD =

x 4 3 x

A baseball field is in the shape of a square. The distance between each pair of bases along the edge of the square is 90 feet. What is the distance between home plate and second base? _________ \(2 feet

90

Each leg of a 45°-45°-90° triangle measures 14 cm. What is the length of the hypotenuse?

D. 14\(2 cm