Question

The diagram shows a simple bridge, which is supported by four steel cables.

Answer 1

(a)

In the given diagram,

∠α and ∠β can be determined using trigonometric functions,

tan α = Opposite side/Adjacent side

⇒ tan α = 4/6

⇒ tan α = 2/3

⇒ α = tan^-1 (2/3)

⇒ α = 33.7°

Similarly,

tan (α + β) = 4+4/6

⇒ tan (α + β) = 8/6

⇒ tan (α + β) = 4/3

⇒ (α + β) = tan^-1 (4/3) = 53.1°

⇒ 33.7 + β = 53.1°

⇒ β = 19.4°

(b)

For the cables adjacent to the perpendicular height, i.e., adjacent to ∠α, on both the sides

Cable length^2 = 4^2 + 6^2 .............................. (Pythagoras theorem)

⇒ Cable length^2 = 16 + 36

⇒ Cable length^2 = 52

⇒ Cable length = 7.21 m

For the cables far from the perpendicular, on both the sides,

Cable length^2 = 6^2 + 8^2 .............................. (Pythagoras theorem)

⇒ Cable length^2 = 36 + 64

⇒ Cable length^2 = 100

⇒ Cable length = 10 m

What is Trigonometric Function?

• The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions.
• In other words, these trig functions provide the relationship between a triangle's angles and sides.
• There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
• The main division of trigonometric functions is into sine, cosine, and tangent angles. Additionally, the three fundamental functions can be used to derive the cotangent, secant, and cosecant functions.
• Basically, compared to the fundamental trigonometric functions, the other three functions are frequently used.
• The lengths of the adjacent and opposing sides are compared to determine the tangent function.

To learn more about Trigonometric Functions, refer to:

brainly.com/question/14746686

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