Answer:
x = 2879.4 m
Explanation:
Given:
A right-angled triangle with one side and a known angle
To find:
the value of x
To determine x, we need to apply the alternate angles to get the angle in the triangle
Using an illustration:
angle = 10°
opposite = side opposite the angle = 500m
hypotenuse = x
To get x, we will apply sine ratio (SOH):
[tex]sin\text{ 10\degree = }\frac{opposite}{hypotenuse}[/tex]
[tex]\begin{gathered} sin\text{ 10\degree = }\frac{500}{x} \\ cross\text{ multiply:} \\ x(sin\text{ 10\degree\rparen = 500} \\ x\text{ = }\frac{500}{sin\text{ 10\degree}} \end{gathered}[/tex]
[tex]\begin{gathered} x\text{ = }\frac{500}{0.173648} \\ \\ x\text{ = 2879.3882} \\ \\ To\text{ the nearest tenth, x = 2879.4} \end{gathered}[/tex]
