Question

Question
1
A)
Use the image to answer the question.
Use trigonometric ratios to solve the following problem. Shaina, who is 5 feet, 6 inches tall, is standing20 feet from the base of a tree when she sees a pileated woodpecker at the top of the tree. The bird isat an angle of elevation of 68 degrees above Shaina’s line of sight. What is the height of the tree?
(1 point)
55 feet
240 inches
66 feet
680 inches
Question
2
Question
3
A)
Salvador and Armando use a land surveying tool, a clinometer, to determine the angle of depressionfrom their position on a bridge to a person in a boat on the water. They know the bridge is 110 feetabove the water and the angle of depression is 40 degrees. How far (to the nearest foot) horizontally isthe boat from Salvador and Armando?
(1 point)
71 feet
131 feet
144 feet
48 feet
A)
A 20-foot-tall flag pole casts a shadow that is 15 feet long. Which of the following correctly uses thePythagorean Theorem to solve for the distance from the top of the flag pole to the tip of its shadow?
(1 point)
25 feet
13.2 feet
35 feet
625 feet
Question
4
A)
Use the image to answer the question.
An isosceles triangle,
, has the measurements
. The segment
is thealtitude of
, and
. Which of the following correctly applies thePythagorean Theorem to find
x
?
(1 point)
△ABC AB = BC = 12 BH
△ABC BH = AH = CH = x
x
=
6
2
–
√
x
=
6
x
=
72
x
=
12
2
–
√
Question
5
A)
Use the image to answer the question.
Tyrese is building a ramp up to his home. He knows the height of the ramp is 2 feet. If the angle ofelevation of the ramp is 20°, how long does the ramp have to be?
(1 point)
0.68 feet
2.13 feet
5.85 feet
5.49 feet

Answer 1

Here are the answers with brief work:

1) Tree height
- From Shaina’s eye level: tan(68°) = (tree top above her eyes) / 20
- tree top above eyes = 20·tan(68°) ≈ 52.10 ft. Add Shaina’s height 5.5 ft → total ≈ 57.60 ft ≈ 691 in.
- Closest choice: 680 inches.

2) Horizontal distance to boat
- tan(40°) = 110 / distance → distance = 110 / tan(40°) ≈ 131.2 ft.
- Choice: 131 feet.

3) Flagpole top to tip of shadow
- Hypotenuse = sqrt(20^2 + 15^2) = sqrt(400+225) = sqrt(625) = 25 ft.
- Choice: 25 feet.

4) Isosceles triangle — correct Pythagorean setup
- For right triangle ABH: AB^2 = AH^2 + BH^2, so 12^2 = x^2 + BH^2.
- (If BH were given as 6, then x = sqrt(12^2 − 6^2) = sqrt(108) = 6√3.)

5) Ramp length
- sin(20°) = opposite/hypotenuse = 2 / length → length = 2 / sin(20°) ≈ 5.85 ft.
- Choice: 5.85 feet.