The distance from the top of the Sunshine Skyway Bridge to the boat is 305.1 feet.
The values of all trigonometric functions dependent on the value of the ratio of sides of a right-angled triangle are known as trigonometric ratios. The trigonometric ratios of a right-angled triangle's sides with regard to any of its acute angles are known as that angle's trigonometric ratios.
The three sides of the right-angled triangle are:
Hypotenuse (the longest side)
Perpendicular (opposite side to the angle)
Base (Adjacent side to the angle)
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
The trigonometry ratios for a specific angle ‘θ’ is given below:
Trigonometric Ratios:
Sin θ = Perpendicular/Hypotenuse
Cos θ = Base/Hypotenuse
Tan θ = Perpendicular/Base or Sin θ/Cos θ
Cot θ = Base/Perpendicular or 1/tan θ
Sec θ = Hypotenuse/Base or 1/cos θ
Cosec θ = Hypotenuse/Perpendicular or 1/sin θ
Let the tower be AB = 175 feet, with the top of the tower as A.
Let the top of the boat be C. We join BC to get a right-angled triangle ABC with ∠B = 90°.
We are told that from the top of the tower, Lexi sees a boat at an angle of depression of 35°, represented as ∠CAD. ∠ACB will be equal to this angle as they are alternate angles.
∴ ∠ACB = 35°.
Let the distance from the top of the boat to the top of the tower be feet, the distance CA, the hypotenuse of the triangle ABC.
∴ By trigonometry, we can say that:
sin 35° = AB/BC
or, 0.5736 = 175/x
or, x = 175/0.5736
or, x = 305.1
∴ The distance from the top of the Sunshine Skyway Bridge to the boat is 305.1 feet.
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