Answer: We can solve this problem using trigonometry and basic geometry. Let's first draw a diagram:
A (top of house)
/|
/ | h
/ |
/ |
/θ1 |
/ |
/ |
/ |
/ |
/ |
/ |
/ |
/ |
/ |
B (top of column)
| d
|
|
|
C (bottom of column)
We are given that angle theta 1 (θ1) is 45 degrees, angle theta 2 (θ2) is 60 degrees, and the height of the column BC is 95.62 meters. We want to find the height of the house AB, which we'll call "h".
First, we can use trigonometry to find the length of segment CD. Since we know angle θ2 and the length of BC, we can use the tangent function:
tan(θ2) = opposite / adjacent
tan(60°) = d / 95.62
d = 95.62 * tan(60°)
d ≈ 165.30 meters
Now we can use the fact that angles ABD and CBD are complementary to find the length of segment AD:
tan(θ1) = opposite / adjacent
tan(45°) = h / (d + 165.30)
h = (d + 165.30) * tan(45°)
h ≈ 165.30 meters
Therefore, the height of the house is approximately 165.30 meters.
Explanation: