The height of the lighthouse is 44 feet.
Step-by-step explanation:
You are given more information than you need.
Use the right triangle concept,
A yacht is anchored 90 feet offshore from the base of a lighthouse.
The angle of elevation from the boat to the top of the lighthouse is 26 degrees.
Using one side length and the angle only:
The trigonometric formula is given as,
tan = height / base
tan[26º] = h ⁄ 90
h = 90 × tan[26º]
h = 43.9 ft
h = 44 feet
Therefore, the height of the lighthouse is 44 feet.
The height of the lighthouse = 44 m
The distance between the yacht and the base of the lighthouse, d = 90 feet
The angle of elevation from the boat to the top of the lighthouse, θ = 26 degrees
Let the height of the lighthouse be represented by h
We can find the height by using the tangent formula
[tex]tan \theta = \frac{Opposite}{Adjacent} \\\\Opposite = h\\\\Adjacent = 90 \\\\\theta = 26^0\\\\tan 26 = \frac{h}{90} \\\\0.4877 = \frac{h}{90}\\\\h = 0.4877 \times 90\\\\h = 43.89 m[/tex]
h = 44 m (to the nearest whole number)
The height of the lighthouse = 44 m
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