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Right Triangles and Trigonometry

Math · Geometry and Trigonometry · 31 questions · every one comes with a full explanation.

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  1. 1Triangle above is a right triangle, and . What is the length of side ?Hard · Geometry and Trigonometry
  2. 2One angle is a right angle. The measure of a second angle is x°. The length of the hypotenuse is 23. The length of the leg opposite the angle with measure x° is 16. A note indicateHard · Geometry and Trigonometry
  3. 3A graphic designer is creating a logo for a company. The logo is shown in the figure above. The logo is in the shape of a trapezoid and consists of three congruent equilateral triaHard · Geometry and Trigonometry
  4. 4The perimeter of an equilateral triangle is 624 centimeters. The height of this triangle is k3 centimeters, where k is a constant. What is the value of k ?Hard · Geometry and Trigonometry
  5. 5In the figure above, . If and , what is the length of ?Hard · Geometry and Trigonometry
  6. 6An isosceles right triangle has a hypotenuse of length 58 inches. What is the perimeter, in inches, of this triangle?Hard · Geometry and Trigonometry
  7. 7An isosceles right triangle has a perimeter of 94 + 94 2 inches. What is the length, in inches, of one leg of this triangle?Hard · Geometry and Trigonometry
  8. 8RS=440 ST=384 TR=584 The side lengths of right triangle R S T are given. Triangle R S T is similar to triangle U V W , where S corresponds to V and T correspHard · Geometry and Trigonometry
  9. 9A right triangle has legs with lengths of 24 centimeters and 21 centimeters. If the length of this triangle's hypotenuse, in centimeters, can be written in the form 3d, where d Hard · Geometry and Trigonometry
  10. 10RS=20 ST=48 TR=52 The side lengths of right triangle RST are given. Triangle RST is similar to triangle UVW, where S corresponds to V and T corresponds to W . What is the valHard · Geometry and Trigonometry
  11. 11In triangle RST above, point W (not shown) lies on . What is the value of ?Hard · Geometry and Trigonometry
  12. 12Triangle A B C is similar to triangle D E F , where A corresponds to D and C corresponds to F . Angles C and F are right angles. If tanA=3 and DF=125, what is the lHard · Geometry and Trigonometry
  13. 13The length of a rectangle's diagonal is 3 17 , and the length of the rectangle's shorter side is 3 . What is the length of the rectangle's longer side?Hard · Geometry and Trigonometry
  14. 14A square is inscribed in a circle. The radius of the circle is 2022 inches. What is the side length, in inches, of the square?Hard · Geometry and Trigonometry
  15. 15Triangle ABC is similar to triangle DEF, where angle A corresponds to angle D and angles C and F are right angles. The length of AB¯ is 2.9 times the length of DE¯. If tanA=21Hard · Geometry and Trigonometry
  16. 16In a right triangle, the tangent of one of the two acute angles is . What is the tangent of the other acute angle?Hard · Geometry and Trigonometry
  17. 17Triangle A B C is similar to triangle D E F , where angle A corresponds to angle D and angle C corresponds to angle F . Angles C and F are right angles. If tan Hard · Geometry and Trigonometry
  18. 18In the figure above, is parallel to . What is the length of ?Hard · Geometry and Trigonometry
  19. 19In triangle J K L , cos K =2451 and angle J is a right angle. What is the value of cos L ?Hard · Geometry and Trigonometry
  20. 20A triangle with angle measures 30°, 60°, and 90° has a perimeter of . What is the length of the longest side of the triangle?Hard · Geometry and Trigonometry