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Trigonometry. Can someone help? (Do as many as you can please)

Trigonometry. Can someone help? (Do as many as you can please)-example-1

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Answer:

1) Let x be the distance from Alberto to the base of the building. Using trigonometry, we have:

tan(70) = 40 / (x + 6)

x + 6 = 40 / tan(70)

x = 40 / tan(70) - 6

x ≈ 11.1 feet

Therefore, Alberto is about 11.1 feet away from the base of the building.

2) Let h be the height of the building. Using trigonometry, we have:

tan(θ) = h / (100 + 1.55)

h = (100 + 1.55) tan(23)

h ≈ 42.9 feet

Therefore, the height of the building is about 42.9 feet.

3) Let θ be the angle of elevation for each ramp. Using trigonometry, we have:

sin(θ) = 22 / 122

θ = sin⁻¹(22/122)

θ ≈ 10.3 degrees

Therefore, the measure of the angle of elevation for each ramp is about 10.3 degrees.

4) Let d be the distance from the boat to the base of the lighthouse. Using trigonometry, we have:

tan(28) = 40 / d

d = 40 / tan(28)

d ≈ 78.5 feet

Therefore, the distance from the base of the lighthouse to the boat is about 78.5 feet.

5) Let x be the distance from General Han Xin's position to the palace. Using trigonometry, we have:

tan(35) = x / 800

x = 800 tan(35)

x ≈ 595.4 meters

Therefore, the palace is about 595.4 meters away from General Han Xin's position.

6) Let h be the height of the clouds. Using trigonometry, we have:

tan(80) = h / 165

h = 165 tan(80)

h ≈ 702.4 meters

Therefore, the clouds are about 702.4 meters high.

Explanation:

User ManuParra
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