1. Unit 2 Review Questions

2. Find the value of x
X=12

3. Tell if the measures 7, 11, and 15 can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right.
acute

4. Find the values of the variables
Find the values of the variables. Give your answers in simplest radical form.
x = 10 and y = 20

5. Find the values of the variables
Find the values of the variables. Give your answers in simplest radical form.
X = 𝟗 𝟐 𝟐

6. Use a special right triangle to write each trigonometric ratio
as a fraction.
cos 60° sin 45°
cos 60 =½
Sin 45 = 𝟐 𝟐

7. Find the unknown measures. Round lengths to the nearest
hundredth and angle measures to the nearest degree.
DE ≅5.7; m∠D≅68°; m∠F≅22°

8. A plane is flying at an altitude of 14,500 ft
A plane is flying at an altitude of 14,500 ft. The angle of depression from the plane to a control tower is 15. What is the horizontal distance from the plane to the tower? Round to the nearest foot.
≅54,115 ft

9. A woman is standing 12 ft from a sculpture
A woman is standing 12 ft from a sculpture. The angle of elevation from her eye to the top of the sculpture is 30, and the angle of depression to its base is 22. How tall is the sculpture to the nearest foot?
12 ft

10. A surveyor 50 meters from the base of a cliff measures the angle of elevation to the top of the cliff as 72°. What is the height of the cliff? Round to the nearest meter.
154 m

11. To the nearest degree, what is m∠A?
53°

12. Determine the perimeter of a square with a diagonal of 72 centimeters.24

13. Write the tangent of ∠T as a fraction.
𝟒 𝟑

14. The ladder, represented by line segment AB , is 17 feet long.
What is the measure of angle A, the
angle that the ladder makes with a
horizontal line?
64°

15. An equilateral triangle has an altitude of 21 inches
An equilateral triangle has an altitude of 21 inches. What is the side length of the triangle?
14 𝟑

16. A ladder 15 feet from the base of a window that 35 feet high
A ladder 15 feet from the base of a window that 35 feet high. What is the length of the ladder to the nearest foot?
38 ft

17. It is recommended that for a height of 20 inches, a wheelchair ramp be 19 feet long. What is the value of x to the nearest tenth?
18.9 ft

18. To secure an outdoor canopy, a 64-inch cord is extended from the top of a vertical pole to the ground. If the cord makes a 60° angle with the ground, how tall is the pole?
or ≅55.4 in

19. A hiking trail has a slope of 7 32
A hiking trail has a slope of What is the measure of the angle that the trail makes with a horizontal line? Round to the nearest degree.
12°

20. Some mountains in the Alps are very steep and have a grade of 42.9%.
To the nearest degree, what angle do
these mountains make with a
horizontal line?
23°

21. Find x and y
x = 12 and y = 12 3