Fadhil berdiri dengan jarak 24 m dari sebuah pohon dan melihat puncak pohon dengan sudut pandang 30°. Jika tinggi Fadhil diukur dari tanah sampai ke mata 150 cm, maka tinggi pohon tersebut adalah …. 1,5+123 meter 1,5+83 meter 1,5+82 meter 13,5 meter 9,5 meter

Mathematics

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Step-by-step solution

5 steps

  1. Convert Fadhil's height to meters.

    Fadhil's height from the ground to his eyes is 150 cm.

    150 cm=1.5 m150 \text{ cm} = 1.5 \text{ m}

  2. Identify the known values for the trigonometric calculation.

    The distance from Fadhil to the tree is the adjacent side of the right-angled triangle, d=24 md = 24 \text{ m}.
    The angle of elevation is θ=30∘\theta = 30^\circ.
    Let h′h' be the height of the tree above Fadhil's eye level. This is the opposite side of the triangle.

  3. Use the tangent function to find h′h'.

    The tangent of an angle in a right-angled triangle is the ratio of the opposite side to the adjacent side:

    tan⁡(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} tan⁡(30∘)=h′24\tan(30^\circ) = \frac{h'}{24}

    We know that tan⁡(30∘)=13=33\tan(30^\circ) = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}.

    33=h′24\frac{\sqrt{3}}{3} = \frac{h'}{24}

    Solve for h′h':

    h′=24×33h' = 24 \times \frac{\sqrt{3}}{3} h′=83 mh' = 8\sqrt{3} \text{ m}

  4. Calculate the total height of the tree.

    The total height of the tree (HH) is the height above Fadhil's eye level plus Fadhil's eye height.

    H=h′+1.5H = h' + 1.5 H=83+1.5 mH = 8\sqrt{3} + 1.5 \text{ m}

  5. Compare the result with the given options.

    The calculated height is 1.5+831.5 + 8\sqrt{3} meters. This matches one of the options.

    The final answer is \boxed{\text{1,5+8\sqrt{3} meter}}.

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