Question

More math help pls. :)

Answer 1

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:

brainly.com/question/2217700