Answer:
1. 6.69ft
2. x=33.5
3. x=14.0
4. x=12
Step-by-step explanation:
Use the sine ratio to find y.
Recall the mnemonics SOH-CAH-TOA
[tex]\sin \theta =\frac{Opposite}{Hypotenuse}[/tex]
Substitute the values to get:
[tex]\sin 26.5\degree =\frac{y}{15}[/tex]
Solve for y
[tex]y=15\sin 26.5\degree[/tex]
[tex]y=6.69ft[/tex]
2. Apply the sine ratio again
[tex]\sin \x=\frac{Opposite}{Hypotenuse}[/tex]
Substitute the values to get:
[tex]\sin \x=\frac{32}{58}[/tex]
[tex]\sin \x=0.5517[/tex]
[tex]x=\sin^{-1}(0.5517)[/tex]
[tex]x=33.5\degree[/tex]
3. Apply the tangent ratio
[tex]\tan x=\frac{Opposite}{Adjacent}[/tex]
Substitute the values to get
[tex]\tan x=\frac{5}{20}[/tex]
[tex]\tan x=\frac{1}{4}[/tex]
[tex]\tan x=0.25[/tex]
[tex]x=\tan {-1}(0.25)[/tex]
[tex]x=14.0\degree[/tex]
4. This is an isosceles right triangle. Therefore the second leg is also [tex]6\sqrt{2}[/tex]
Now apply the Pythagoras Theorem to obtain:
[tex]x^2=(6\sqrt{2})^2+(6\sqrt{2})^2[/tex]
[tex]x^2=72+72[/tex]
[tex]x^2=144\implies x=12[/tex]
