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A robot is on the surface of Mars. The angle of depression from a camera in the robot to a rock on the surface of Mars is 13.11^(@). The camera is 181.0cm above the surface. How far is the camera from the rock? The camera is ◻ cm from the rock. (Round to the neare tenth as needed.)

A robot is on the surface of Mars. The angle of depression from a camera in the robot to a rock on the surface of Mars is 13.11∘ 13.11^{\circ} . The camera is 181.0 cm 181.0 \mathrm{~cm} above the surface. How far is the camera from the rock?\newlineThe camera is □ \square cm \mathrm{cm} from the rock.\newline(Round to the neare tenth as needed.)

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Q. A robot is on the surface of Mars. The angle of depression from a camera in the robot to a rock on the surface of Mars is 13.11∘ 13.11^{\circ} . The camera is 181.0 cm 181.0 \mathrm{~cm} above the surface. How far is the camera from the rock?\newlineThe camera is □ \square cm \mathrm{cm} from the rock.\newline(Round to the neare tenth as needed.)
  1. Understand and Visualize: Understand the problem and visualize the scenario.\newlineWe are given the angle of depression from the camera to the rock, which is 13.1113.11 degrees. The camera is 181.0181.0 cm above the surface of Mars. We need to find the horizontal distance from the camera to the rock. This forms a right triangle with the angle of depression at the camera, the height of the camera as one leg, and the distance to the rock as the other leg.
  2. Convert to Elevation: Convert the angle of depression to the angle of elevation.\newlineThe angle of elevation from the base of the camera to the camera is equal to the angle of depression, which is 13.1113.11 degrees. This is because the angle of depression from the camera to the rock is congruent to the angle of elevation from the rock to the camera.
  3. Use Trigonometry: Use trigonometry to find the distance to the rock.\newlineWe can use the tangent of the angle of elevation to find the horizontal distance to the rock. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the camera) to the adjacent side (distance to the rock).\newlineLet's denote the distance to the rock as dd. Then we have:\newlinetan⁡(13.11°)=oppositeadjacent\tan(13.11°) = \frac{\text{opposite}}{\text{adjacent}}\newlinetan⁡(13.11°)=181.0 cmd\tan(13.11°) = \frac{181.0\,\text{cm}}{d}
  4. Solve for Distance: Solve for the distance dd. To find dd, we rearrange the equation: d=181.0 cmtan⁡(13.11∘)d = \frac{181.0 \, \text{cm}}{\tan(13.11^\circ)} Now we calculate the value using a calculator. d≈181.0 cmtan⁡(13.11∘)d \approx \frac{181.0 \, \text{cm}}{\tan(13.11^\circ)} d≈181.0 cm0.232d \approx \frac{181.0 \, \text{cm}}{0.232} d≈780.172 cmd \approx 780.172 \, \text{cm}
  5. Round to Nearest Tenth: Round the distance to the nearest tenth. d≈780.2d \approx 780.2 cm

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