Unit 4.3: Right Triangles Unit TEST

Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support beam that will connect the ends of the two boards measures 20 feet. Which is true regarding the triangular frame?

B. It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.

Which equation can be used to solve for c?

B. c = 5 / cos(35o)

Each leg of a 45°-45°-90° triangle measures 12 cm. What is the length of the hypotenuse?

C. 12 cm

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. 13 ft

Which is a perfect square?

C. 36

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth.

C. 381.3 cm^2

An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?

C. 42.0 cm

The equation tan-1 (8.9/7.7) = x can be used to find the measure of angle LKJ. What is the measure of angle LKJ? Round to the nearest whole degree.

C. 49°

Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches. What is the greatest possible whole-number length of the unknown side?

C. 7 inches

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. What is the smallest possible perimeter of the triangle, rounded to the nearest tenth?

C. 72.4 in.

Which set of side lengths is a Pythagorean triple?

C. 9, 40, 41

Joey is building a frame for a sandbox. The sandbox is going to be a quadrilateral that has the lengths shown. If the diagonal of the sandbox measures 14 feet, which best describes the shape of the sandbox?

C. a quadrilateral, because angle C and angle X are acute

Triangle ABC is a right triangle and cos(22.6o)= b/13. Solve for b and round to the nearest whole number. Which equation correctly uses the value of b to solve for a?

C. an(22.6o) = a/12

What are the angle measures of triangle VUW?

C. m∠V = 60°, m∠U = 90°, m∠W = 30°

In which triangle is the value of x equal to tan−1 (3.1/5.2)? (Images may not be drawn to scale.)

D.

The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

D. 5.7 cm

Which equation can be used to find the measure of angle LJK?

D. cos(x) = 15/10

Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?

acute, because 10^2+12^2>15^2

Which equation can be used to find the length of AC?

A. (10)sin(40o) = AC

The hypotenuse of a 45°-45°-90° triangle measures 22(sqr.root)2 units. What is the length of one leg of the triangle?

A. 11 units

The longest side of an obtuse triangle measures 20 cm. The two shorter sides measure x cm and 3x cm. Rounded to the nearest tenth, what is the greatest possible value of x?

A. 6.3

Which equation can be used to solve for the measure of angle ABC?

A. tan(x) = 2.4/10

The diagonal of rectangle ABCD measures 2 inches in length. What is the length of line segment AB?

B. (sqr.root) 3 inches

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. 12(sqr.root)3 ft

The length of the hypotenuse, line segment GH, in triangle GJH measures 6 cm. Line segment JH measures 2 cm. Which is the approximate measure of angle JGH?

B. 19.5°

The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle?

B. 2(sqr.root)2 cm

The equation sin(25o)= 9/c can be used to find the length of AB. What is the length of ? Round to the nearest tenth.

B. 21.3 in.

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

B. 3.2 inches

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?

B. 39.4°

Which expressions can be used to find m<BAC? Check all that apply.

cos-1 (6.9/12) sin-1 (9.8/12) tan-1 (9.8/6.9)