# ACT Math - Triangles: Help and Review Chapter Exam

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

### Page 1

#### Question 1 1. If the long leg of a 30-60-90 triangle is 23, approximately how long is the short leg?

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Question 2
2.
The isosceles triangle pictured below shows one angle measuring 40 degrees. What is the measure of angle *x*?

#### Question 3 3. In the picture shown below, there are three lines marking each side of the triangle. These lines give the indication that the triangle is:

#### Question 4 4. A baseball diamond has 90 feet between each base. How far will the catcher (standing at home plate) throw the ball across the diagonal to the second baseman at 2nd base?

#### Question 5 5. Determine if triangle VEZ is similar to triangle MAG.

### Page 2

#### Question 6 6. If the leg of a 45-45-90 triangle is 19, approximately how long is the hypotenuse?

#### Question 7 7. Greg is standing next to a 40 ft. tree. The sun casts a 5 ft. shadow of Greg, who is 6.4 ft. tall. How long is the tree's shadow?

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Question 8
8.
Triangle POX has a perimeter of 15 inches. Side PO is 2 less than *x*, an unknown number. Side OX is 2 greater than *x*, and side PX can be expressed as 2*x* - 5. Find the length of each side of triangle POX (in the order PO, OX, PX).

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Question 9
9.
In the right triangle pictured below, what is the value of angle *x*?

#### Question 10 10. Sergeant Ketchup's billiards room is 15 feet wide and 25 feet long. How many square feet is the room in total?

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#### Question 11 11. Which of these could not be the side lengths of a 3-4-5 right triangle?

#### Question 12 12. If the hypotenuse of a 45-45-90 triangle is 31, approximately how long is the leg?

#### Question 13 13. Jeremy's goal is to jog around the neighborhood park four times. If the park has four sides and each side is 100 meters, how many meters will Jeremy jog?

#### Question 14 14. Given triangles DAR and KMR. What is the value of y?

#### Question 15 15. What's wrong with this triangle?

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#### Question 16 16. The hypotenuse of a right triangle is 30. The lengths of the two shorter sides are x and x + 10. Is this a 3-4-5 right triangle?

#### Question 17 17. What is the Pythagorean Theorem and how is it used?

#### Question 18 18. What is the area of ABCDE, as shown in the diagram?

#### Question 19 19. You are standing at the point (2,3) on a graph. Which point is closer: (-1,2) or (4,6)?

#### Question 20 20. A right triangle has one leg that measures 7 inches, and the second leg measures 10 inches. How long is the hypotenuse?

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#### Question 21 21. Which of the following is true?

#### Question 22 22. A right triangle has one leg that measures 13 centimeters, and the hypotenuse is 17 centimeters. How long is the missing leg?

#### Question 23 23. A triangle has side lengths 0.3, 0.4, and 0.5. Do these side lengths form a Pythagorean Triple?

#### Question 24 24. Is triangle ABC similar to triangle DEF?

#### Question 25 25. What type of triangle is pictured?

### Page 6

#### Question 26 26. Brad places a marker on the ground 10 ft. away from the base of a tree at a botanical garden. He walks back towards the tree until he is standing 4 ft. away from the marker, and he is 6 ft. tall. Assuming that the top of Brad's head, the top of the tree, and the marker form two simliar triangles, how tall is the tree?

#### Question 27 27. What is the area of the pictured rectangle?

#### Question 28 28. Joan is building a fence for her triangular garden. One side of the garden is 8 feet long, the second side is 10 feet long, and the third side is 12 feet long. If fencing costs $10 per foot, how much will Joan spend on fencing for her garden?

#### Question 29 29. If the hypotenuse of a 30-60-90 triangle is 18, approximately how long is the short leg?

#### Question 30 30. The two shorter sides of a right triangle are 21 and 28. Without using the Pythagorean Theorem, can you find the long side?

#### ACT Math - Triangles: Help and Review Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!