The point `A` is 25 m from the base of a building. The angle of elevation from `A` to the top of the building is 38°.
- Show that the height of the building is approximately 19.5 m. (1 mark)
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- A car is parked 62 m from the base of the building.
What is the angle of depression from the top of the building to the car?
Give your answer to the nearest minute. (2 marks)
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Show Worked Solution
i. `text(Need to prove height (h) ) ~~ 19.5\ text(m)`
| `tan 38^@` | `= h/25` |
| `h` | `= 25 xx tan38^@` |
| `= 19.5321…` | |
| `~~ 19.5\ text(m)\ \ text(… as required.)` |
| ii. |
`text(Let)\ \ /_ \ text(Elevation (from car) ) = theta`
♦♦ Mean mark 33%
MARKER’S COMMENT: If >30 “seconds”, round to the higher “minute”.
MARKER’S COMMENT: If >30 “seconds”, round to the higher “minute”.
| `tan theta` | `= h/62` |
| `= 19.5/62` | |
| `= 0.3145…` | |
| `:. theta` | `= 17.459…` |
| `= 17°27^{′}33^{″}..` | |
| `=17°28^{′}\ \ text{(nearest minute)}` |
`:./_ \ text(Depression to car) =17°28^{′}\ \ text{(alternate to}\ theta text{)}`