Question

Problem 1) The triangle below is a special right triangle with 45-45-90 angles. What is the value of the hypotenuse, x?



(1 point)
Responses

x = 2
x = 2

x = 18
x = 18

x = 5
x = 5

x = 20
x = 20
Question 2
Problem 2) A park ranger is looking upward at a tower that is 45 feet tall. The angle of depression from the tower to the ranger is 40°. How far is the ranger from the tower? Note: the dashed line is parallel to the ground.



(1 point)
Responses

x = 53.6 feet
x = 53.6 feet

x = 21.2 feet
x = 21.2 feet

x = 98.1 feet
x = 98.1 feet

x = 11.5 feet
x = 11.5 feet
Question 3
Problem 3) A ladder is leaning against a wall at a 60° angle to the ground. The base of the ladder is 30 feet away from the wall. What is the height of the wall? Hint: use right triangle trigonometry.



(1 point)
Responses

x = 24.57
x = 24.57

x = 11.36
x = 11.36

x = 51.96
x = 51.96

x = 89.43
x = 89.43
Question 4
Problem 4) What is the value of sin(α
) for the triangle below?



(1 point)
Responses

817
8 over 17

815
8 over 15

1715
17 over 15

158
15 eighths
Question 5
Problem 5) An observer is staring upward 35° at the top of a tree. The observer is standing at point A, which is 47 feet away from the base of the tree. How tall is the tree?



(1 point)
Responses

x = 9.7 feet
x = 9.7 feet

x = 21.2 feet
x = 21.2 feet

x = 12.4 feet
x = 12.4 feet

x = 32.9 feet
x = 32.9 feet
Question 6
Problem 6) What are the ratios of the side lengths in a 30-60-90 special right triangle, such as the one shown below?



(1 point)
Responses

1:1:2–√
1:1:square root of 2

1:2:3–√
1:2:square root of 3

1:2:5
1:2:5

6:8:9
6:8:9
Question 7
Problem 7) What are the ratios of the side lengths in a 45-45-90 special right triangle, such as the one shown below?



(1 point)
Responses

1:2:3–√
1:2:square root of 3

1:2:4
1:2:4

2:5:6
2:5:6

1:1:2–√
1:1:square root of 2
Question 8
Problem 8) A car must drive 2000 meters up a ramp to reach the top of a hill. The angle of elevation is 22°. How tall is the hill?



(1 point)
Responses

x = 801 meters
x = 801 meters

x = 749 meters
x = 749 meters

x = 905 meters
x = 905 meters

x = 679 meters
x = 679 meters
Question 9
Problem 9) A triangular garden has side-lengths of 33 feet and 24 feet, with an angle of 62° between them. What is the area of the garden? Note: this is a non-right triangle.



(1 point)
Responses

Area = 125 ft2
Area = 125 ft2

Area = 190 ft2
Area = 190 ft2

Area = 350 ft2
Area = 350 ft2

Area = 470 ft2
Area = 470 ft2
Question 10
Problem 10) Which ratio in triangle △DEF would correspond to the ratio 53
in triangle △ABC? Assume both figures are similar right triangles.



(2 points)
0 / 10000 Word Limit
Question 11
Problem 11) The right triangle below has two acute angles with measures of 3x and 2x+10. What is the value of x? Please solve the problem and include a brief explanation of your reasoning.



(2 points)

Answer 1

I can solve these, but Problems 1 and 10 need the diagrams (or which sides/vertices correspond) to pick the exact choice. For the others, here are the answers and brief work:

Problem 1) I can’t determine x without the figure or the given leg length — please upload or tell me the side lengths/labels.

Problem 2) x = 53.6 feet.
- tan 40° = opposite/adjacent = 45/x → x = 45 / tan 40° ≈ 53.6 ft.

Problem 3) x = 51.96.
- Height = adjacent * tan 60° = 30 * √3 ≈ 30(1.732) = 51.96.

Problem 4) 8/17.
- The sine is opposite/hypotenuse; the triangle gives opposite = 8, hypotenuse = 17 → sin(α) = 8/17.

Problem 5) x = 32.9 feet.
- tan 35° = height / 47 → height = 47·tan 35° ≈ 47(0.7002) ≈ 32.9 ft.

Problem 6) Ratios for a 30-60-90 triangle are 1 : √3 : 2 (short leg : long leg : hypotenuse).
- (Select the choice that represents 1:√3:2.)

Problem 7) 1 : 1 : √2.
- (45-45-90 triangle: legs equal, hypotenuse = leg·√2.)

Problem 8) x = 749 meters.
- height = 2000·sin 22° ≈ 2000(0.3746) ≈ 749 m.

Problem 9) Area = 350 ft².
- Area = (1/2)(33)(24)·sin 62° = 396·sin 62° ≈ 396(0.8829) ≈ 349.6 ≈ 350 ft².

Problem 10) I need the labeling correspondence between △ABC and △DEF. If, for example, AB/AC = 5/3 and A↔D, B↔E, C↔F, then the corresponding ratio is DE/DF = 5/3. Provide the triangle labels or indicate which side ratio in △ABC is 5/3 and I’ll give the exact corresponding ratio in △DEF.

Problem 11) x = 16.
- In a right triangle the two acute angles add to 90°. So 3x + (2x + 10) = 90 → 5x + 10 = 90 → 5x = 80 → x = 16.

If you upload the figures or state which sides correspond in Problems 1 and 10, I’ll finish those.