Answer:
Side O: 8.9
Side H: 14.2
Step-by-step explanation:
Because this is a right triangle (notice the square on the bottom left of the picture) then we can use our trig functions. Using SOH-CAH-TOA (Sine: Opposite/Hypotenuse, Cosine: Adjacent/Hypotenuse, and Tangent: Opposite/Adjacent) then we can solve this.
The problem gives us an angle of 39 degrees and a side of 11 units, so we will base our trig functions on that. To find O, we will use Tangent because we are given our adjacent side and need to find the opposite side (or O). Set the equation up where [tex]tan(39)=\frac{O}{11}[/tex] where if we solve this we get [tex]O=tan(39)*11[/tex]. This leaves us with a value of 8.9 for O (rounded to the 10th.)
Next, we can solve for H by using cosine. With 11 being the adjacent side once again and H being the hypotenuse, we get the equation [tex]cos(39)=\frac{11}{H}[/tex] where this can be rearranged into [tex]H=\frac{11}{cos(39)}[/tex]. This leaves us with a value of 14.2 for H (also rounded to the 10th.)
