ANSWER
See below
EXPLANATION
To solve the triangle means to find all sides and angles.
The right triangle has an angle of 38 degrees and an opposite leg of 12 yards
The third angle is 90-38=52°
We use the sine ratio to find the hypotenuse, h.
[tex] \sin(38 \degree) = \frac{opposite}{hypotenuse} [/tex]
[tex] \sin(38 \degree) = \frac{12}{h} [/tex]
[tex]h = \frac{12}{ \sin(38) } [/tex]
[tex]h = 19.49[/tex]
The hypotenuse is 19.49 yards to the nearest hundredth.
We can find the adjacent leg using the cosine ratio.
[tex] \cos(38) = \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos(38) = \frac{a}{19.49} [/tex]
[tex]a = 19.49 \cos(39) [/tex]
[tex]a = 15.36[/tex]
to the nearest hundredth.
