Answer: 33.7
Explanation:
Let the height of the house be h, and the distance from the foot of the rock to the house be x.
From the given information, we have the following diagram:
```
*
/ \
/ \
/ 63° \
/ \
/θ \
A ----------------------- B
70m x
Angle A = 60° (complementary to the angle of elevation of the foot of the house)
Angle B = 63° (angle of elevation of the top of the house)
Using trigonometry, we have:
tan(63°) = h/x ----(1) (for triangle AOB)
tan(60°) = h/(x + 70) ----(2) (for triangle ABD)
Solving equations (1) and (2) simultaneously, we get:
h = (70 tan(63°) - 70 tan(60°)) meters
h ≈ 33.7 meters (rounded to one decimal place)
Therefore, the height of the house is approximately 33.7 meters.