Simplify the steps
The value of x in the triangle using the principle of Pythagoras is 2879.4 meters
Given the right angle triangle :
The angle of elevation = 10°
Opposite side = 500 m
x = hypotenus
Recall :
SOHCAHTOA
Using the relation :
Sin θ = opposite / hypotenus
Sin 10° = 500 / x
Cross multiply :
x(sin 10°) = 500
0.1736481x = 500
x = 500 / 0.1736481
x = 2879.39 meters
Simplified Steps:
1. In the right angle triangle, the angle of elevation is 10° and the opposite side is 500 m.
2. Use the sine function: sin θ = opposite / hypotenuse.
3. Substitute the values: sin 10° = 500 / x.
4. Cross multiply: x(sin 10°) = 500.
5. Simplify: 0.1736481x = 500.
6. Solve for x: x = 500 / 0.1736481.
7. Calculate: x ≈ 2879.39 meters.