Question

Please answer #5 that’s shown in the picture. Please Ignore the pencil work that is already on the page. Thank you.

Answer 1

We have to use the trigonometric ratios to find the lengths of the missing sides.

We know the measure of the angle O and the length of its opposite side DT.

We can find the value of the hypotenuse OT with the ratio:

`\begin{gathered} \sin (O)=\frac{\text{Opposite}}{\text{Hypotenuse}}=(DT)/(OT) \\ OT=(DT)/(\sin(O))=(15)/(\sin (72\degree))\approx(15)/(0.951)\approx15.77 \end{gathered}`

We can find the length of the adyacent side OD with the ratio:

`\begin{gathered} \tan (O)=\frac{\text{Opposite}}{\text{Adyacent}}=(DT)/(OD) \\ OD=(DT)/(\tan(O))=(15)/(\tan (72\degree))\approx(15)/(3.078)\approx4.87 \end{gathered}`

To complete the missing angles, we take into account that one of the angles, D, is a right angle, so its measure is 90°.

Angle T and angle O are complementary, so they add 90° between the two.

Then, angle T will have a measure of 90-72 = 18°.

Answer:

Sides:

OD = 4.87

OT = 15.77

Angles:

m∠O = 90°

m∠T = 18°