Geometry EOC Review 5

Belle is hanging streamers for her brother’s surprise birthday party. She secures two streamers of different lengths at the peak of the ceiling. The center of the floor is directly underneath the ceiling peak. The distance along the floor from the center of the room to where the first streamer is attached is 6 feet. The second streamer is attached to the floor further from the center of the floor than the first streamer. The distance between the streamers is 𝑥 feet and the length of the second streamer is 𝑦 feet. The angle formed between the second streamer and the floor is 𝜃. Select all of the equations that are true to the nearest tenth based on the diagram.

Given the diagram showing two right triangles, complete the following statements:

Statement A. sin 33.7° = $$\frac{BC}{?}$$ ​ ​ (a)  

Statement B. sin 33.7° = $$\frac{?}{DF}$$ ​ (b)  

Statement C. $$\frac{BC}{AC}=\frac{?}{?}$$ ​ (c)  

A company is requesting equilateral tiles to be made for their new office floor. If the height of the tile is approximately 10.4 inches, what is the length of the sides of the triangle?

The same company, mentioned in the previous question, decides they also want to use half of a square with the side the same length as the height of the equilateral triangle. What is the length of the hypotenuse of the triangle formed from taking half of the square? Leave answer in simplest radical form.

The logo of a local construction company contains an equilateral triangle. The height of the triangle is 10 units. What is the length of the measure of each side of the triangle? Leave answer in simplest radical form.

The right triangle ABC is shown. Angle B is the right angle and the length of AB is 1.5 centimeters and the length of BC is 3.1 centimeters. Determine the measure of angle A. Round answer to the nearest tenth.

The right triangle ABC is shown. Angle B is the right angle and the length of AB is 1.5 centimeters and the length of BC is 3.1 centimeters. Determine the measure of angle C. Round answer to the nearest tenth.

The right triangle ABC is shown. Angle B is the right angle and the length of AB is 1.5 centimeters and the length of BC is 3.1 centimeters. Determine the length of AC. Round answer to the nearest tenth.

Triangle ABC has two of its vertices located at (-4, -1) and (3, -3). If the centroid is at (-1, 13), what is the third vertex of the triangle?

(a)  

Triangle ABC has two of its vertices located at (-4, -1) and (3, -3). If the centroid is at (-1, 13), determine whether triangle 𝐴𝐵𝐶 is a right triangle based on its angle measures and side lengths.

Triangle ABC ​ (a)   a right triangle because sides ​ (b)  

perpendicular.