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Cardo is on top of a 15-meter cliff. He knows that it is 11.7 meters from the bottom of the cliff to the near bank of the river and that the angle of depression is 52°. The angle of depression to the far bank is 38°. Find the width of the river to nearest tenth of a meter.



Answer :

Milliorian

Answer:

y ≈ 6.3 meters

Step-by-step explanation:

Step 1: Draw a diagram of the situation, labeling the known distances and angles.

Step 2: Let x be the distance from the near bank to the point directly below Cardo. Use the tangent function to relate the angle of depression, the height of the cliff, and x. = tan(52°) = 15/x => x = 15/tan(52°)

Step 3: Let y be the width of the river. Use the tangent function to relate the angle of depression to the far bank, the height of the cliff, and x + y. = tan(38°) = 15/(x + y)

Step 4: Substitute the expression for x from step 2 into the equation from step 3: = tan(38°) = 15/(15/tan(52°) + y)

Step 5: Solve for y. = y ≈ 6.3 meters

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