Answer:
76 ft
Step-by-step explanation:
We can model the given scenario as a right triangle where:
- The base of the triangle represents the horizontal distance between the surveyor's camera and the gas station (76 ft).
- The height of the triangle corresponds to the height of the gas station.
- The angle formed between the base and the hypotenuse measures 45°.
The interior angles of any triangle add up to 180°. Given that one of the acute angles in the right triangle is 45°, it follows that the other acute angle is also 45°. Therefore, the right triangle in this scenario is a special case known as a 45-45-90 triangle.
In a 45-45-90 triangle, the sides are in the ratio 1 : 1 : √2. This means that both legs of the triangle are of equal length, and the hypotenuse is √2 times the length of either leg.
In this scenario, the base and the height of the right triangle represent its legs. As the base of the triangle is 76 ft, the height is also 76 ft.
Therefore, the height of the gas station is 76 ft.
