Amelia is looking at the top of a lighthouse. She knows she is 30 feet from the base of the lighthouse. If she is 5.5 feet tall and the angle of elevation is 34° how tall is the
lighthouse? Write only the number rounded to the nearest tenth of a foot.

25.7 feet

Step-by-step explanation:

We are solving a right angled triangle.

We are the Trigonometric function of Tangent

tan θ = Opposite side/Adjacent

Angle of Elevation = θ = 34°

Opposite side = Height

Adjacent = 30 feet

tan 34° = Opposite side/30 feet.

Opposite side = tan 34° × 30 feet

Opposite side = 20.235255505 feet

The height of the light house =

Opposite side(height) + Amelia's height

20.235255505 feet + 5.5 feet

= 25.735255505 feet

Approximately to the nearest tenth ≈ 25.7 feet

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.