The approximate angle of elevation of the sun is 47°.
What do we mean by trigonometric ratios?
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
How do we solve the given question?
Let Billy be AB.
∴ AB = 74 inches.
Let BC be Billy's shadow.
∴ BC = 70 inches.
Now ABC together makes a right-angled triangle with ∠B = 90°.
At C, we can see the elevation, and let that be θ.
Let the angle of elevation be θ.
∴ tan θ = AB/BC = 74/70 = 1.0571 = tan 46.59°.
∴ θ = 46.59° ≈ 47°
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