Chapter 9 Review

Carson and Jocee are building a triangular garden. They want to find the area of their isosceles triangle. (See Diagram 5)

• 10 square units

• 15 square units

• 20 square units

• 25 square units

Jaxson and Taylee are exploring a mysterious triangular island. They need to find the values of x and y to unlock a hidden treasure. Can you help them by finding the values of x and y in simplest form?

• x = 2, y = 3

• x = 1, y = 4

• x = 3, y = 2

• x = 4, y = 1

Taylee, Carson, and McKay are on a treasure hunt! They found three mysterious sticks of different lengths. Can these sticks form a triangle? If they can, what kind of triangle will it be?

• Yes, it forms an acute triangle

• Yes, it forms an obtuse triangle

• Yes, it forms a right triangle

• No, it does not form a triangle

Taylee the daring pilot took her helicopter on an adventure! First, she soared vertically into the sky, climbing 325 meters. Then, with a swift turn, she zoomed 500 meters east. Can you calculate how far Taylee is from her original take-off point?

• Taylee's helicopter is approximately 583 meters from the starting point.

• Taylee's helicopter is approximately 600 meters from the starting point.

• Taylee's helicopter is approximately 700 meters from the starting point.

• Taylee's helicopter is approximately 800 meters from the starting point.

Bodie is designing a fun wheelchair ramp for his friend Carson. The ramp is 4.2 meters long and rises up 0.7 meter. Can you help Bodie find the angle of elevation to the nearest tenth of a degree?

• 9.6°

• 10.0°

• 9.5°

• 9.8°

Join Jocee on an adventurous flight journey! She flies 470 miles due west from Chicago, Illinois, to Omaha, Nebraska. Then, she takes a 437-mile flight to St. Louis, Missouri. Finally, she completes her triangular adventure with a 300-mile flight back to Chicago. Can you determine if the triangle formed by Jocee's trip is acute, right, or obtuse?

• Acute

• Right

• Obtuse

McKay and Carson went on an adventure to Kennywood Park. While there, they marveled at the thrilling Phantom’s Revenge roller-coaster. McKay, being curious, examined the inclined section of the track. He noticed that the ramp section rose at a 45° angle with the horizontal section and connected at the top of the hill with a segment 100 feet long. These pieces formed a right angle at the top of the hill. Can you help McKay find x, the length from the point of inclination to the bottom of the hill?

• 50 feet

• 70.71 feet

• 100 feet

• 141.42 feet

Eli is standing in a park and looks up at a 55° angle to see the top of a mysterious tower. The vertical distance from the ground to his eyes is 5.5 feet, and he's standing 57 feet away from the tower. Can you help Eli estimate the height of this intriguing structure?

• Approximately 50 feet

• Approximately 60 feet

• Approximately 70 feet

• Approximately 80 feet

Nolan, an avid bird watcher, spots a bird perched on top of a lamppost. The angle formed between the lamppost and the line extending from the bird's feet to Nolan's feet, as he stands at a distance, is 55°. If Nolan is standing 25 feet away from the lamppost, can you help him estimate the height of the lamppost?

• 14.3 feet

• 20.5 feet

• 17.9 feet

• 21.4 feet

During a friendly math challenge, Carson asked Jocee, "Using a trigonometric identity, can you tell me the value of sin(45°)?"

• 0.5

• 0.7071

• 0.866

• 1