Answer:
12.511 3dp
Step-by-step explanation:
Diagram - See Attachment - Not drawn accurately.
Using trigonometic equations, we have the opposite and we want to find the hypotenuse.
Sinx = opp/hyp
Substitute X with 46 and opp with 9.
Sin46 = 9/hyp
Rearrange to get the hypotenuse on its own
Sin46 = 9/hyp
Sin46 * hyp = 9
hyp = 9/Sin46
hyp = 12.511 (3dp)
The length of the slide is 12.51147 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 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 bottom of the slide be C, bottom of the vertical part of the slide be B, and the top be A.
Now, we get a right-angled triangle ABC, with a right angle at B.
By question, we have AB = 9 feet, ∠C = 46°, and we need to find AC.
Applying the trigonometric ratio of sine, we get
sin ∠C = AB/AC
or, sin 46° = 9/AC
or, AC = 9/sin 46°
or, AC = 9/0.71934 = 12.51147
∴ The length of the slide is 12.51147 feet.
Learn more about Trigonometric Ratios at
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