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On the grid provided, draw the graph of y = 50x. Daudi was standing on a balcony. He observed a ball on the ground, 47 m from the foot of the building. The angle of depression of the ball from Daudi's position was 15°. Calculate the height from the ground to where Daudi was.

Mathematics

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Answer

b

32.91 m\text{32.91 m}

Graph of y = 50x

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Key points of y = 50x
Pointxy
x-intercept00

Step-by-step solution

8 steps

Here are the solutions for the problems.

1. Completing the table and drawing the graph for y=50xy = 50x.

Part a· 2 steps

Complete the table using the equation y=50xy = 50x.

  1. Substitute the given xx values into the equation y=50xy = 50x to find the corresponding yy values.

    • For x=0.5x = 0.5: y=50×0.5=25y = 50 \times 0.5 = 25
    • For x=2x = 2: y=50×2=100y = 50 \times 2 = 100
  2. Fill in the table with the calculated values.

    x00.511.52y0255075100\begin{array}{|c|c|c|c|c|c|} \hline x & 0 & 0.5 & 1 & 1.5 & 2 \\ \hline y & 0 & 25 & 50 & 75 & 100 \\ \hline \end{array}

Part b

32.91 m\text{32.91 m}

On the grid provided, draw the graph of y=50xy = 50x.

  1. Plot the points from the completed table on the grid

    $(0,0)$, $(0.5, 25)$, $(1, 50)$, $(1.5, 75)$, and $(2, 100)$.

  2. Draw a straight line connecting these points.

    The line should pass through the origin $(0,0)$ and extend to the last plotted point $(2,100)$.

    2. Calculating the height of Daudi's position.

  3. Identify the known values and the unknown.

    • Horizontal distance from the foot of the building to the ball (adjacent side) = 47 m.
    • Angle of depression = 35∘35^\circ. This is equal to the angle of elevation from the ball to Daudi's position.
    • Height from the ground to Daudi's position (opposite side) = HH.
  4. Use the tangent trigonometric ratio, which relates the opposite side, adjacent side, and the angle.

    tan⁡(θ)=OppositeAdjacent\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} tan⁡(35∘)=H47 m\tan(35^\circ) = \frac{H}{47 \text{ m}}
  5. Solve for HH.

    H=47 m×tan⁡(35∘)H = 47 \text{ m} \times \tan(35^\circ) H=47 m×0.7002075...H = 47 \text{ m} \times 0.7002075... H=32.90975... mH = 32.90975... \text{ m}
  6. Round the height to a suitable number of decimal places (e.g., two decimal places).

    H=32.91 mH = \boxed{\text{32.91 m}}

    2 zimekamilika. Zimebaki 3 leo — tuma inayofuata.

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