By using trigonometric relations, we will see that x = 9.97°.
How to find the missing angle?
First, we need to find the bottom cathetus of the smaller triangle, we will use the relation:
Tan(θ) = (opposite cathetus)/(adjacent cathetus).
Where:
- θ = 26°
- Adjacent cathetus = k
- Opposite cathetus = 55ft.
Replacing that we get:
Tan(26°) = 50ft/k
Solving this for k, we get:
k = 55ft/tan(26°) = 112.8 ft
Now, we can see that the longer triangle adds 200ft to this cathetus, so now we will have:
- angle = x
- opposite cathetus = 55ft
- adjacent cathetus = 112.8ft + 200ft = 312.8ft.
Then we have:
Tan(x) = (55ft/312.8ft)
Using the inverse tangent function in both sides, we get:
x = Atan(55ft/312.8ft) = 9.97°
If you want to learn more about right triangles, you can read:
https://brainly.com/question/2217700
